Bovier, Anton 1957
Overview
Works:  181 works in 336 publications in 2 languages and 5,328 library holdings 

Genres:  Conference papers and proceedings Academic theses 
Roles:  Author, Editor, Other, Creator, Thesis advisor 
Publication Timeline
.
Most widely held works by
Anton Bovier
Mathematical statistical physics : École d'Été de Physique des Houches : Session LXXXIII : 429 July, 2005 : ESF Summer
School : École thematique du CNRS by
Anton Bovier(
)
20 editions published in 2006 in English and Undetermined and held by 1,460 WorldCat member libraries worldwide
The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians
20 editions published in 2006 in English and Undetermined and held by 1,460 WorldCat member libraries worldwide
The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians
Statistical mechanics of disordered systems : a mathematical perspective by
Anton Bovier(
)
21 editions published between 2006 and 2012 in English and held by 774 WorldCat member libraries worldwide
"This selfcontained book is a graduatelevel introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a twosemester course on mathematical statistical mechanics. It assumes only some basic knowledge of classical physics; on the mathematics side, the reader should have a good working knowledge of graduatelevel probability theory."Jacket
21 editions published between 2006 and 2012 in English and held by 774 WorldCat member libraries worldwide
"This selfcontained book is a graduatelevel introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a twosemester course on mathematical statistical mechanics. It assumes only some basic knowledge of classical physics; on the mathematics side, the reader should have a good working knowledge of graduatelevel probability theory."Jacket
Spin glasses by
Erwin Bolthausen(
)
16 editions published in 2007 in English and Undetermined and held by 656 WorldCat member libraries worldwide
"This collection of stateoftheart review papers witten by leading experts in the field covers the topic from a wide variety of angles. The topics covered are mean field spin glasses, including a pedagogical account of Talagrand's proof of the Parisi solution, short range spin glasses, emphasizing the open problem of the relevance of the meanfield theory for lattice models, and the dynamics of spin glasses, in particular the problem of ageing in mean field models." "The book will serve as a concise introduction to the state of the art of spin glass theory, usefull to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics."Jacket
16 editions published in 2007 in English and Undetermined and held by 656 WorldCat member libraries worldwide
"This collection of stateoftheart review papers witten by leading experts in the field covers the topic from a wide variety of angles. The topics covered are mean field spin glasses, including a pedagogical account of Talagrand's proof of the Parisi solution, short range spin glasses, emphasizing the open problem of the relevance of the meanfield theory for lattice models, and the dynamics of spin glasses, in particular the problem of ageing in mean field models." "The book will serve as a concise introduction to the state of the art of spin glass theory, usefull to both graduate students and young researchers, as well as to anyone curious to know what is going on in this exciting area of mathematical physics."Jacket
Spin glasses : statics and dynamics, Summer School, Paris 2007 by
Anne Boutet Monvel(
)
15 editions published in 2009 in English and held by 454 WorldCat member libraries worldwide
This book contains a collection of texts ranging from a basic introduction to the mathematical theory of spin glasses to stateoftheart reports on current research, written by leading experts in the field. It provides a unique single reference volume that will guide the novice into the field and present an overview of recent result to the experts. The subject matter covers mean field theory of spin glasses, short range spin glasses as well as other models of statistical mechanics in random media, such as polymers in disordered potentials. Besides equilibrium statistical mechanics, nonequilibrium properties such as ageing are addressed. The focus of the book is on mathematically rigorous aspects of these topics. The book is intended for graduate students and researchers
15 editions published in 2009 in English and held by 454 WorldCat member libraries worldwide
This book contains a collection of texts ranging from a basic introduction to the mathematical theory of spin glasses to stateoftheart reports on current research, written by leading experts in the field. It provides a unique single reference volume that will guide the novice into the field and present an overview of recent result to the experts. The subject matter covers mean field theory of spin glasses, short range spin glasses as well as other models of statistical mechanics in random media, such as polymers in disordered potentials. Besides equilibrium statistical mechanics, nonequilibrium properties such as ageing are addressed. The focus of the book is on mathematically rigorous aspects of these topics. The book is intended for graduate students and researchers
Mathematical Statistical Physics : Lecture Notes of the Les Houches Summer School 2005 by
Anton Bovier(
)
2 editions published in 2006 in English and held by 364 WorldCat member libraries worldwide
Features the proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics which give an overview on this fast developing area of interest to both physicists and mathematicians. This book also presents an introduction to the field of math with many interdisciplinary connections in physics, biology, and computer science
2 editions published in 2006 in English and held by 364 WorldCat member libraries worldwide
Features the proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics which give an overview on this fast developing area of interest to both physicists and mathematicians. This book also presents an introduction to the field of math with many interdisciplinary connections in physics, biology, and computer science
Metastability : a potentialtheoretic approach by
Anton Bovier(
)
12 editions published between 2015 and 2016 in English and held by 343 WorldCat member libraries worldwide
Metastability is a widespread phenomenon in the dynamics of nonlinear systems  physical, chemical, biological or economic  subject to the action of temporal random forces typically referred to as noise. This monograph provides a concise presentation of mathematical approach to metastability based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focus on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finitestate Markov chains, finitedimensional diffusions and stochastic partial differential equations, via meanfield dynamics with and without disorder, to stochastic spinflip and particlehopping dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability
12 editions published between 2015 and 2016 in English and held by 343 WorldCat member libraries worldwide
Metastability is a widespread phenomenon in the dynamics of nonlinear systems  physical, chemical, biological or economic  subject to the action of temporal random forces typically referred to as noise. This monograph provides a concise presentation of mathematical approach to metastability based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focus on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finitestate Markov chains, finitedimensional diffusions and stochastic partial differential equations, via meanfield dynamics with and without disorder, to stochastic spinflip and particlehopping dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability
Random walks, random fields, and disordered systems by
Anton Bovier(
)
10 editions published in 2015 in English and held by 321 WorldCat member libraries worldwide
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spinglass) systems, a detailed analysis of weakly selfavoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on twodimensional loopsoup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields
10 editions published in 2015 in English and held by 321 WorldCat member libraries worldwide
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spinglass) systems, a detailed analysis of weakly selfavoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on twodimensional loopsoup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields
Mathematical aspects of spin glasses and neural networks by
Anton Bovier(
Book
)
13 editions published between 1996 and 1998 in English and held by 244 WorldCat member libraries worldwide
13 editions published between 1996 and 1998 in English and held by 244 WorldCat member libraries worldwide
Gaussian processes on trees : from spin glasses to branching Brownian motion by
Anton Bovier(
Book
)
10 editions published between 2016 and 2017 in English and held by 164 WorldCat member libraries worldwide
Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of meanfield spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to meanfield spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the FKPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a selfcontained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics
10 editions published between 2016 and 2017 in English and held by 164 WorldCat member libraries worldwide
Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of meanfield spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to meanfield spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the FKPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a selfcontained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics
Methods of contemporary mathematical statistical physics by
Marek Biskup(
)
8 editions published in 2009 in English and held by 42 WorldCat member libraries worldwide
This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. An introductory chapter on lattice spin models is useful as a background for other lectures of the collection. The topics include new results on phase transitions for gradient lattice models (with introduction to the techniques of the reflection positivity), stochastic geometry reformulation of classical and quantum Ising models, the localization/delocalization transition for directed polymers. A general rigorous framework for theory of metastability is presented and particular applications in the context of Glauber and Kawasaki dynamics of lattice models are discussed. A pedagogical account of several recently discussed topics in nonequilibrium statistical mechanics with an emphasis on general principles is followed by a discussion of kinetically constrained spin models that are reflecting important peculiar features of glassy dynamics
8 editions published in 2009 in English and held by 42 WorldCat member libraries worldwide
This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. An introductory chapter on lattice spin models is useful as a background for other lectures of the collection. The topics include new results on phase transitions for gradient lattice models (with introduction to the techniques of the reflection positivity), stochastic geometry reformulation of classical and quantum Ising models, the localization/delocalization transition for directed polymers. A general rigorous framework for theory of metastability is presented and particular applications in the context of Glauber and Kawasaki dynamics of lattice models are discussed. A pedagogical account of several recently discussed topics in nonequilibrium statistical mechanics with an emphasis on general principles is followed by a discussion of kinetically constrained spin models that are reflecting important peculiar features of glassy dynamics
Disordered Systems and random geometry : polymers, spin glasses, interfaces by
Anton Bovier(
Book
)
9 editions published in 1986 in 3 languages and held by 29 WorldCat member libraries worldwide
9 editions published in 1986 in 3 languages and held by 29 WorldCat member libraries worldwide
Contributions to the potential theoretic approach to metastability with applications to the random field CurieWeissPotts
model by Martin Slowik(
)
1 edition published in 2012 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 16 WorldCat member libraries worldwide
Metastability A PotentialTheoretic Approach by
Anton Bovier(
)
2 editions published in 2015 in English and held by 16 WorldCat member libraries worldwide
2 editions published in 2015 in English and held by 16 WorldCat member libraries worldwide
Hydrodynamic limit for the A + B → Ø model(
)
1 edition published in 2006 in English and held by 9 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 9 WorldCat member libraries worldwide
Sharp asymptotics for Kawasaki dynamics on a finite box with open boundary by
Anton Bovier(
Book
)
2 editions published in 2004 in English and held by 7 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 7 WorldCat member libraries worldwide
The opinion game : stock price evolution from microscopic market modelling by
Anton Bovier(
Book
)
2 editions published in 2004 in English and held by 6 WorldCat member libraries worldwide
We propose a class of Markovian agent based models for the time evolution of a share price in an interactive market. The models rely on a microscopic description of a market of buyers and sellers who change their opinion about the stock value in a stochastic way. The actual price is determined in realistic way by matching (clearing) offers until no further transactions can be performed. Some analytic results for a noninteracting model are presented. We also propose basic interaction mechanisms and show in simulations that these already reproduce certain particular features of prices in real stock markets
2 editions published in 2004 in English and held by 6 WorldCat member libraries worldwide
We propose a class of Markovian agent based models for the time evolution of a share price in an interactive market. The models rely on a microscopic description of a market of buyers and sellers who change their opinion about the stock value in a stochastic way. The actual price is determined in realistic way by matching (clearing) offers until no further transactions can be performed. Some analytic results for a noninteracting model are presented. We also propose basic interaction mechanisms and show in simulations that these already reproduce certain particular features of prices in real stock markets
Metastability in stochastic dynamics of disorderd mean field models(
Book
)
2 editions published between 1998 and 2000 in English and held by 6 WorldCat member libraries worldwide
2 editions published between 1998 and 2000 in English and held by 6 WorldCat member libraries worldwide
Spectral characterisation of ageing : the REMlike trap model by
Anton Bovier(
Book
)
2 editions published in 2004 in English and held by 6 WorldCat member libraries worldwide
We review the ageing phenomenon in the context of simplest trap model, Bouchaud's REMlike trap model from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalised exactly. Using this result, we derive closed expressions for correlation functions in terms of complex contour integrals that permit an easy investigation into their large time asymptotics in the thermodynamic limit. We also give a 'grand canonical' representation of the model in terms of the Markov process on a Poisson point process . In this context we analyse the dynamics on various time scales
2 editions published in 2004 in English and held by 6 WorldCat member libraries worldwide
We review the ageing phenomenon in the context of simplest trap model, Bouchaud's REMlike trap model from a spectral theoretic point of view. We show that the generator of the dynamics of this model can be diagonalised exactly. Using this result, we derive closed expressions for correlation functions in terms of complex contour integrals that permit an easy investigation into their large time asymptotics in the thermodynamic limit. We also give a 'grand canonical' representation of the model in terms of the Markov process on a Poisson point process . In this context we analyse the dynamics on various time scales
Universality of the REM for dynamics of meanfield spin glasses by
Gérard Ben Arous(
Book
)
2 editions published in 2007 in English and held by 6 WorldCat member libraries worldwide
We consider a version of a Glauber dynamics for a $p$spin SherringtonKirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the $N$dimensional hypercube. We show that, for any $p /geq 3$ and any inverse temperature $/beta>0$, there exist constants $/g_0>0$, such that for all exponential time scales, $/exp(/gamma N)$, with $/g/leq /g_0$, the properly rescaled /emphclock process (timechange process), converges to an $/a$stable subordinator where $/a=/g//b2<1$. Moreover, the dynamics exhibits aging at these time scales with timetime correlation function converging to the arcsine law of this /hbox$/alpha$stable subordinator. In other words, up to rescaling, on these time scales (that are shorter than the equilibration time of the system), the dynamics of $p$spin models ages in the same way as the REM, and by extension Bouchaud's REMlike trap model, confirming the latter as a universal aging mechanism for a wide range of systems. The SK model (the case $p=2$) seems to belong to a different universality class
2 editions published in 2007 in English and held by 6 WorldCat member libraries worldwide
We consider a version of a Glauber dynamics for a $p$spin SherringtonKirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the $N$dimensional hypercube. We show that, for any $p /geq 3$ and any inverse temperature $/beta>0$, there exist constants $/g_0>0$, such that for all exponential time scales, $/exp(/gamma N)$, with $/g/leq /g_0$, the properly rescaled /emphclock process (timechange process), converges to an $/a$stable subordinator where $/a=/g//b2<1$. Moreover, the dynamics exhibits aging at these time scales with timetime correlation function converging to the arcsine law of this /hbox$/alpha$stable subordinator. In other words, up to rescaling, on these time scales (that are shorter than the equilibration time of the system), the dynamics of $p$spin models ages in the same way as the REM, and by extension Bouchaud's REMlike trap model, confirming the latter as a universal aging mechanism for a wide range of systems. The SK model (the case $p=2$) seems to belong to a different universality class
Universality of REMlike ageing in mean field spin glasses by
Gérard Ben Arous(
Book
)
2 editions published in 2007 in English and held by 6 WorldCat member libraries worldwide
Aging has become the paradigm to describe dynamical behavior of glassy systems, and in particular spin glasses. Trap models have been introduced as simple caricatures of effective dynamics of such systems. In this Letter we show that in a wide class of mean field models and on a wide range of time scales, aging occurs precisely as predicted by the REMlike trap model of Bouchaud and Dean. This is the first rigorous result about aging in mean field models except for the REM and the spherical model
2 editions published in 2007 in English and held by 6 WorldCat member libraries worldwide
Aging has become the paradigm to describe dynamical behavior of glassy systems, and in particular spin glasses. Trap models have been introduced as simple caricatures of effective dynamics of such systems. In this Letter we show that in a wide class of mean field models and on a wide range of time scales, aging occurs precisely as predicted by the REMlike trap model of Bouchaud and Dean. This is the first rigorous result about aging in mean field models except for the REM and the spherical model
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Related Identities
 Hollander, F. den (Frank) Other Contributor Editor
 Bolthausen, Erwin 1945 Author Editor
 Boutet de MonvelBerthier, Anne 1948 Author Editor
 Enter, Aernout Van Other Editor
 Dunlop, Francois Other Editor
 Dalibard, Jean Other Editor
 Kotecký, R. (Roman) Editor
 Biskup, Marek Author Editor
 Černý, Jiří Editor
 CojaOghlan, Amin
Useful Links
Associated Subjects
Brownian motion processes Combinatorial analysis Computer scienceMathematics Distribution (Probability theory) Gaussian processes Markov processes Mathematical physics Mathematical statistics Mathematics Mechanical engineering Neural networks (Computer science)Mathematics Phase transformations (Statistical physics) Physics Probabilities Random variables Random walks (Mathematics) Spin glasses Spin glassesMathematics Stability Statistical mechanics Statistical physics Statistics Structural analysis (Engineering) System theory