Probability And Statistical Physics In Two And More Dimensions

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Probability and Statistical Physics in Two and More Dimensions

Clay Mathematics Institute. Summer School
Probability and Statistical Physics in Two and More Dimensions Book PDF

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
Page : 481 pages
File Size : 44,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821868638

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Probability and Statistical Physics in Two and More Dimensions by Clay Mathematics Institute. Summer School Pdf

This volume is a collection of lecture notes for six of the ten courses given in Buzios, Brazil by prominent probabilists at the 2010 Clay Mathematics Institute Summer School, ``Probability and Statistical Physics in Two and More Dimensions'' and at the XIV Brazilian School of Probability. In the past ten to fifteen years, various areas of probability theory related to statistical physics, disordered systems and combinatorics have undergone intensive development. A number of these developments deal with two-dimensional random structures at their critical points, and provide new tools and ways of coping with at least some of the limitations of Conformal Field Theory that had been so successfully developed in the theoretical physics community to understand phase transitions of two-dimensional systems. Included in this selection are detailed accounts of all three foundational courses presented at the Clay school--Schramm-Loewner Evolution and other Conformally Invariant Objects, Noise Sensitivity and Percolation, Scaling Limits of Random Trees and Planar Maps--together with contributions on Fractal and Multifractal properties of SLE and Conformal Invariance of Lattice Models. Finally, the volume concludes with extended articles based on the courses on Random Polymers and Self-Avoiding Walks given at the Brazilian School of Probability during the final week of the school. Together, these notes provide a panoramic, state-of-the-art view of probability theory areas related to statistical physics, disordered systems and combinatorics. Like the lectures themselves, they are oriented towards advanced students and postdocs, but experts should also find much of interest.

Probability and Statistical Physics in St. Petersburg

V. Sidoravicius,S. Smirnov
Probability and Statistical Physics in St Petersburg Book PDF

Author : V. Sidoravicius,S. Smirnov
Publisher : American Mathematical Soc.
Page : 471 pages
File Size : 40,8 Mb
Release : 2016-04-28
Category : Combinatorial analysis
ISBN : 9781470422486

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Probability and Statistical Physics in St. Petersburg by V. Sidoravicius,S. Smirnov Pdf

This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.

Sojourns in Probability Theory and Statistical Physics - III

Vladas Sidoravicius
Sojourns in Probability Theory and Statistical Physics III Book PDF

Author : Vladas Sidoravicius
Publisher : Springer Nature
Page : 341 pages
File Size : 45,6 Mb
Release : 2019-10-17
Category : Mathematics
ISBN : 9789811503023

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Sojourns in Probability Theory and Statistical Physics - III by Vladas Sidoravicius Pdf

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Sojourns in Probability Theory and Statistical Physics - I

Vladas Sidoravicius
Sojourns in Probability Theory and Statistical Physics I Book PDF

Author : Vladas Sidoravicius
Publisher : Springer Nature
Page : 338 pages
File Size : 55,9 Mb
Release : 2019-10-17
Category : Mathematics
ISBN : 9789811502941

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Sojourns in Probability Theory and Statistical Physics - I by Vladas Sidoravicius Pdf

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.

Statistical Mechanics of Lattice Systems

Sacha Friedli,Yvan Velenik
Statistical Mechanics of Lattice Systems Book PDF

Author : Sacha Friedli,Yvan Velenik
Publisher : Cambridge University Press
Page : 643 pages
File Size : 43,9 Mb
Release : 2017-11-23
Category : Mathematics
ISBN : 9781107184824

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Statistical Mechanics of Lattice Systems by Sacha Friedli,Yvan Velenik Pdf

A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

The Genesis of the Langlands Program

Julia Mueller,Freydoon Shahidi
The Genesis of the Langlands Program Book PDF

Author : Julia Mueller,Freydoon Shahidi
Publisher : Cambridge University Press
Page : 451 pages
File Size : 41,8 Mb
Release : 2021-08-05
Category : Mathematics
ISBN : 9781108710947

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The Genesis of the Langlands Program by Julia Mueller,Freydoon Shahidi Pdf

A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.

Random Graphs, Phase Transitions, and the Gaussian Free Field

Martin T. Barlow,Gordon Slade
Random Graphs Phase Transitions and the Gaussian Free Field Book PDF

Author : Martin T. Barlow,Gordon Slade
Publisher : Springer Nature
Page : 421 pages
File Size : 48,8 Mb
Release : 2019-12-03
Category : Mathematics
ISBN : 9783030320119

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Random Graphs, Phase Transitions, and the Gaussian Free Field by Martin T. Barlow,Gordon Slade Pdf

The 2017 PIMS-CRM Summer School in Probability was held at the Pacific Institute for the Mathematical Sciences (PIMS) at the University of British Columbia in Vancouver, Canada, during June 5-30, 2017. It had 125 participants from 20 different countries, and featured two main courses, three mini-courses, and twenty-nine lectures. The lecture notes contained in this volume provide introductory accounts of three of the most active and fascinating areas of research in modern probability theory, especially designed for graduate students entering research: Scaling limits of random trees and random graphs (Christina Goldschmidt) Lectures on the Ising and Potts models on the hypercubic lattice (Hugo Duminil-Copin) Extrema of the two-dimensional discrete Gaussian free field (Marek Biskup) Each of these contributions provides a thorough introduction that will be of value to beginners and experts alike.

Introduction to a Renormalisation Group Method

Roland Bauerschmidt,David C. Brydges,Gordon Slade
Introduction to a Renormalisation Group Method Book PDF

Author : Roland Bauerschmidt,David C. Brydges,Gordon Slade
Publisher : Springer Nature
Page : 283 pages
File Size : 55,8 Mb
Release : 2019-10-16
Category : Science
ISBN : 9789813295933

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Introduction to a Renormalisation Group Method by Roland Bauerschmidt,David C. Brydges,Gordon Slade Pdf

This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.

Schramm–Loewner Evolution

Antti Kemppainen
Schramm Loewner Evolution Book PDF

Author : Antti Kemppainen
Publisher : Springer
Page : 145 pages
File Size : 47,7 Mb
Release : 2017-12-22
Category : Science
ISBN : 9783319653297

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Schramm–Loewner Evolution by Antti Kemppainen Pdf

This book is a short, but complete, introduction to the Loewner equation and the SLEs, which are a family of random fractal curves, as well as the relevant background in probability and complex analysis. The connection to statistical physics is also developed in the text in an example case. The book is based on a course (with the same title) lectured by the author. First three chapters are devoted to the background material, but at the same time, give the reader a good understanding on the overview on the subject and on some aspects of conformal invariance. The chapter on the Loewner equation develops in detail the connection of growing hulls and the differential equation satisfied by families of conformal maps. The Schramm–Loewner evolutions are defined and their basic properties are studied in the following chapter, and the regularity properties of random curves as well as scaling limits of discrete random curves are investigated in the final chapter. The book is aimed at graduate students or researchers who want to learn the subject fairly quickly.

Random Walks, Random Fields, and Disordered Systems

Anton Bovier,David Brydges,Amin Coja-Oghlan,Dmitry Ioffe,Gregory F. Lawler
Random Walks Random Fields and Disordered Systems Book PDF

Author : Anton Bovier,David Brydges,Amin Coja-Oghlan,Dmitry Ioffe,Gregory F. Lawler
Publisher : Springer
Page : 239 pages
File Size : 54,5 Mb
Release : 2015-09-21
Category : Science
ISBN : 9783319193397

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Random Walks, Random Fields, and Disordered Systems by Anton Bovier,David Brydges,Amin Coja-Oghlan,Dmitry Ioffe,Gregory F. Lawler Pdf

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 (spin-glass) systems, a detailed analysis of weakly self-avoiding 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 two-dimensional loop-soup 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.

Probability and Phase Transition

G.R. Grimmett
Probability and Phase Transition Book PDF

Author : G.R. Grimmett
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 44,7 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401583268

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Probability and Phase Transition by G.R. Grimmett Pdf

This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability. The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

High-Dimensional Probability

Roman Vershynin
High Dimensional Probability Book PDF

Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 44,6 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781108415194

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High-Dimensional Probability by Roman Vershynin Pdf

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Advances in Disordered Systems, Random Processes and Some Applications

Pierluigi Contucci,Cristian Giardinà
Advances in Disordered Systems Random Processes and Some Applications Book PDF

Author : Pierluigi Contucci,Cristian Giardinà
Publisher : Cambridge University Press
Page : 383 pages
File Size : 47,8 Mb
Release : 2016-12-15
Category : Science
ISBN : 9781107124103

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Advances in Disordered Systems, Random Processes and Some Applications by Pierluigi Contucci,Cristian Giardinà Pdf

This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.

Mathematics Going Forward

Jean-Michel Morel,Bernard Teissier
Mathematics Going Forward Book PDF

Author : Jean-Michel Morel,Bernard Teissier
Publisher : Springer Nature
Page : 629 pages
File Size : 40,9 Mb
Release : 2023-06-14
Category : Mathematics
ISBN : 9783031122446

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Mathematics Going Forward by Jean-Michel Morel,Bernard Teissier Pdf

This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.

Dirichlet Forms and Related Topics

Zhen-Qing Chen,Masayoshi Takeda,Toshihiro Uemura
Dirichlet Forms and Related Topics Book PDF

Author : Zhen-Qing Chen,Masayoshi Takeda,Toshihiro Uemura
Publisher : Springer Nature
Page : 572 pages
File Size : 51,9 Mb
Release : 2022-09-04
Category : Mathematics
ISBN : 9789811946721

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Dirichlet Forms and Related Topics by Zhen-Qing Chen,Masayoshi Takeda,Toshihiro Uemura Pdf

This conference proceeding contains 27 peer-reviewed invited papers from leading experts as well as young researchers all over the world in the related fields that Professor Fukushima has made important contributions to. These 27 papers cover a wide range of topics in probability theory, ranging from Dirichlet form theory, Markov processes, heat kernel estimates, entropy on Wiener spaces, analysis on fractal spaces, random spanning tree and Poissonian loop ensemble, random Riemannian geometry, SLE, space-time partial differential equations of higher order, infinite particle systems, Dyson model, functional inequalities, branching process, to machine learning and Hermitizable problems for complex matrices. Researchers and graduate students interested in these areas will find this book appealing.