Topics In Occupation Times And Gaussian Free Fields
DOWNLOAD
Download Topics In Occupation Times And Gaussian Free Fields PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Topics In Occupation Times And Gaussian Free Fields book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Topics In Occupation Times And Gaussian Free Fields
DOWNLOAD
Author : Alain-Sol Sznitman
language : en
Publisher: European Mathematical Society
Release Date : 2012
Topics In Occupation Times And Gaussian Free Fields written by Alain-Sol Sznitman and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Gaussian processes categories.
This book grew out of a graduate course at ETH Zurich during the spring 2011 term. It explores various links between such notions as occupation times of Markov chains, Gaussian free fields, Poisson point processes of Markovian loops, and random interlacements, which have been the object of intensive research over the last few years. These notions are developed in the convenient setup of finite weighted graphs endowed with killing measures. This book first discusses elements of continuous-time Markov chains, Dirichlet forms, potential theory, together with some consequences for Gaussian free fields. Next, isomorphism theorems and generalized Ray-Knight theorems, which relate occupation times of Markov chains to Gaussian free fields, are presented. Markovian loops are constructed and some of their key properties derived. The field of occupation times of Poisson point processes of Markovian loops is investigated. Of special interest are its connection to the Gaussian free field, and a formula of Symanzik. Finally, links between random interlacements and Markovian loops are discussed, and some further connections with Gaussian free fields are mentioned.
Random Explorations
DOWNLOAD
Author : Gregory F. Lawler
language : en
Publisher: American Mathematical Society
Release Date : 2022-12-06
Random Explorations written by Gregory F. Lawler and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.
The title “Random Explorations” has two meanings. First, a few topics of advanced probability are deeply explored. Second, there is a recurring theme of analyzing a random object by exploring a random path. This book is an outgrowth of lectures by the author in the University of Chicago Research Experiences for Undergraduate (REU) program in 2020. The idea of the course was to expose advanced undergraduates to ideas in probability research. The book begins with Markov chains with an emphasis on transient or killed chains that have finite Green's function. This function, and its inverse called the Laplacian, is discussed next to relate two objects that arise in statistical physics, the loop-erased random walk (LERW) and the uniform spanning tree (UST). A modern approach is used including loop measures and soups. Understanding these approaches as the system size goes to infinity requires a deep understanding of the simple random walk so that is studied next, followed by a look at the infinite LERW and UST. Another model, the Gaussian free field (GFF), is introduced and related to loop measure. The emphasis in the book is on discrete models, but the final chapter gives an introduction to the continuous objects: Brownian motion, Brownian loop measures and soups, Schramm-Loewner evolution (SLE), and the continuous Gaussian free field. A number of exercises scattered throughout the text will help a serious reader gain better understanding of the material.
An Introduction To Random Interlacements
DOWNLOAD
Author : Alexander Drewitz
language : en
Publisher: Springer
Release Date : 2014-05-06
An Introduction To Random Interlacements written by Alexander Drewitz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-06 with Mathematics categories.
This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus. Random interlacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on the torus to random interlacements and the full proof of the percolation phase transition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with the underlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the challenges posed by the long-range correlations present in the model. The aim is to engage the reader in the world of random interlacements by means of detailed explanations, exercises and heuristics. Each chapter ends with short survey of related results with up-to date pointers to the literature.
Random Walks Random Fields And Disordered Systems
DOWNLOAD
Author : Anton Bovier
language : en
Publisher: Springer
Release Date : 2015-09-21
Random Walks Random Fields And Disordered Systems written by Anton Bovier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-21 with Science categories.
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.
In And Out Of Equilibrium 3 Celebrating Vladas Sidoravicius
DOWNLOAD
Author : Maria Eulália Vares
language : en
Publisher: Springer Nature
Release Date : 2021-03-25
In And Out Of Equilibrium 3 Celebrating Vladas Sidoravicius written by Maria Eulália Vares and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-25 with Mathematics categories.
This is a volume in memory of Vladas Sidoravicius who passed away in 2019. Vladas has edited two volumes appeared in this series ("In and Out of Equilibrium") and is now honored by friends and colleagues with research papers reflecting Vladas' interests and contributions to probability theory.
Two Dimensional Random Walk
DOWNLOAD
Author : Serguei Popov
language : en
Publisher: Cambridge University Press
Release Date : 2021-03-18
Two Dimensional Random Walk written by Serguei Popov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-18 with Mathematics categories.
A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
Progress In High Dimensional Percolation And Random Graphs
DOWNLOAD
Author : Markus Heydenreich
language : en
Publisher: Springer
Release Date : 2017-11-22
Progress In High Dimensional Percolation And Random Graphs written by Markus Heydenreich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
This text presents an engaging exposition of the active field of high-dimensional percolation that will likely provide an impetus for future work. With over 90 exercises designed to enhance the reader’s understanding of the material, as well as many open problems, the book is aimed at graduate students and researchers who wish to enter the world of this rich topic. The text may also be useful in advanced courses and seminars, as well as for reference and individual study. Part I, consisting of 3 chapters, presents a general introduction to percolation, stating the main results, defining the central objects, and proving its main properties. No prior knowledge of percolation is assumed. Part II, consisting of Chapters 4–9, discusses mean-field critical behavior by describing the two main techniques used, namely, differential inequalities and the lace expansion. In Parts I and II, all results are proved, making this the first self-contained text discussing high-dime nsional percolation. Part III, consisting of Chapters 10–13, describes recent progress in high-dimensional percolation. Partial proofs and substantial overviews of how the proofs are obtained are given. In many of these results, the lace expansion and differential inequalities or their discrete analogues are central. Part IV, consisting of Chapters 14–16, features related models and further open problems, with a focus on the big picture.
Probability And Statistical Physics In St Petersburg
DOWNLOAD
Author : V. Sidoravicius
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-28
Probability And Statistical Physics In St Petersburg written by V. Sidoravicius and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Combinatorial analysis categories.
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.
Introduction To A Renormalisation Group Method
DOWNLOAD
Author : Roland Bauerschmidt
language : en
Publisher: Springer Nature
Release Date : 2019-10-16
Introduction To A Renormalisation Group Method written by Roland Bauerschmidt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-16 with Science categories.
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.
Lecture Notes On The Gaussian Free Field
DOWNLOAD
Author : Wendelin Werner
language : en
Publisher:
Release Date : 2021
Lecture Notes On The Gaussian Free Field written by Wendelin Werner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.