Probability and Statistical Physics in Two and More Dimensions

Probability and Statistical Physics in Two and More Dimensions
Title Probability and Statistical Physics in Two and More Dimensions PDF eBook
Author Clay Mathematics Institute. Summer School
Publisher American Mathematical Soc.
Pages 481
Release 2012
Genre Mathematics
ISBN 0821868632

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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.

High-Dimensional Probability

High-Dimensional Probability
Title High-Dimensional Probability PDF eBook
Author Roman Vershynin
Publisher Cambridge University Press
Pages 299
Release 2018-09-27
Genre Business & Economics
ISBN 1108415199

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

Probability and Statistical Physics in St. Petersburg

Probability and Statistical Physics in St. Petersburg
Title Probability and Statistical Physics in St. Petersburg PDF eBook
Author V. Sidoravicius
Publisher American Mathematical Soc.
Pages 482
Release 2016-04-28
Genre Mathematics
ISBN 1470422484

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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.

Statistical Mechanics of Lattice Systems

Statistical Mechanics of Lattice Systems
Title Statistical Mechanics of Lattice Systems PDF eBook
Author Sacha Friedli
Publisher Cambridge University Press
Pages 643
Release 2017-11-23
Genre Mathematics
ISBN 1107184827

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

High-Dimensional Statistics

High-Dimensional Statistics
Title High-Dimensional Statistics PDF eBook
Author Martin J. Wainwright
Publisher Cambridge University Press
Pages 571
Release 2019-02-21
Genre Business & Economics
ISBN 1108498027

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A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding.

Statistical Physics of Particles

Statistical Physics of Particles
Title Statistical Physics of Particles PDF eBook
Author Mehran Kardar
Publisher Cambridge University Press
Pages 211
Release 2007-06-07
Genre Science
ISBN 1139464876

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Statistical physics has its origins in attempts to describe the thermal properties of matter in terms of its constituent particles, and has played a fundamental role in the development of quantum mechanics. Based on lectures taught by Professor Kardar at MIT, this textbook introduces the central concepts and tools of statistical physics. It contains a chapter on probability and related issues such as the central limit theorem and information theory, and covers interacting particles, with an extensive description of the van der Waals equation and its derivation by mean field approximation. It also contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set of solutions is available to lecturers on a password protected website at www.cambridge.org/9780521873420. A companion volume, Statistical Physics of Fields, discusses non-mean field aspects of scaling and critical phenomena, through the perspective of renormalization group.

Random Graphs, Phase Transitions, and the Gaussian Free Field

Random Graphs, Phase Transitions, and the Gaussian Free Field
Title Random Graphs, Phase Transitions, and the Gaussian Free Field PDF eBook
Author Martin T. Barlow
Publisher Springer Nature
Pages 421
Release 2019-12-03
Genre Mathematics
ISBN 3030320111

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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.