Markov Paths Loops And Fields

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Markov Paths Loops And Fields

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Author : Yves Le Jan
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-06

Markov Paths Loops And Fields written by Yves Le Jan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-06 with Mathematics categories.

The purpose of these notes is to explore some simple relations between Markovian path and loop measures, the Poissonian ensembles of loops they determine, their occupation fields, uniform spanning trees, determinants, and Gaussian Markov fields such as the free field. These relations are first studied in complete generality for the finite discrete setting, then partly generalized to specific examples in infinite and continuous spaces.

Markov Paths Loops And Fields

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Author : Yves Le Jan
language : en
Publisher: Springer
Release Date : 2011-07-06

Markov Paths Loops And Fields written by Yves Le Jan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-06 with Mathematics categories.

The purpose of these notes is to explore some simple relations between Markovian path and loop measures, the Poissonian ensembles of loops they determine, their occupation fields, uniform spanning trees, determinants, and Gaussian Markov fields such as the fre field. These relations are first studied in complete generality for the finite discrete setting, then partly generalized to specific examples in infinite and continuous spaces.

Intersection Local Times Loop Soups And Permanental Wick Powers

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Author : Yves Le Jan
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-25

Intersection Local Times Loop Soups And Permanental Wick Powers written by Yves Le Jan 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 2017-04-25 with Gaussian processes categories.

Several stochastic processes related to transient Lévy processes with potential densities , that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures endowed with a metric . Sufficient conditions are obtained for the continuity of these processes on . The processes include -fold self-intersection local times of transient Lévy processes and permanental chaoses, which are `loop soup -fold self-intersection local times' constructed from the loop soup of the Lévy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of -th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.

Random Walks And Physical Fields

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Author : Yves Le Jan
language : en
Publisher: Springer Nature
Release Date :

Random Walks And Physical Fields written by Yves Le Jan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

S Minaire De Probabilit S Xlvi

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Author : Catherine Donati-Martin
language : en
Publisher: Springer
Release Date : 2014-12-29

S Minaire De Probabilit S Xlvi written by Catherine Donati-Martin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-29 with Mathematics categories.

Providing a broad overview of the current state of the art in probability theory and its applications, and featuring an article coauthored by Mark Yor, this volume contains contributions on branching processes, Lévy processes, random walks and martingales and their connection with, among other topics, rough paths, semi-groups, heat kernel asymptotics and mathematical finance.

Topics In Occupation Times And Gaussian Free Fields

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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.

Correlated Random Systems Five Different Methods

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Author : Véronique Gayrard
language : en
Publisher: Springer
Release Date : 2015-06-09

Correlated Random Systems Five Different Methods written by Véronique Gayrard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-09 with Mathematics categories.

This volume presents five different methods recently developed to tackle the large scale behavior of highly correlated random systems, such as spin glasses, random polymers, local times and loop soups and random matrices. These methods, presented in a series of lectures delivered within the Jean-Morlet initiative (Spring 2013), play a fundamental role in the current development of probability theory and statistical mechanics. The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Models by N. Kistler, Isomorphism Theorems by J. Rosen and Spectral Properties of Wigner Matrices by B. Schlein. This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake. It is targeted at researchers, in particular PhD students and postdocs, working in probability theory and statistical physics.

S Minaire De Probabilit S L

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Author : Catherine Donati-Martin
language : en
Publisher: Springer Nature
Release Date : 2019-11-19

S Minaire De Probabilit S L written by Catherine Donati-Martin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-19 with Mathematics categories.

This milestone 50th volume of the "Séminaire de Probabilités" pays tribute with a series of memorial texts to one of its former editors, Jacques Azéma, who passed away in January. The founders of the "Séminaire de Strasbourg", which included Jacques Azéma, probably had no idea of the possible longevity and success of the process they initiated in 1967. Continuing in this long tradition, this volume contains contributions on state-of-art research on Brownian filtrations, stochastic differential equations and their applications, regularity structures, quantum diffusion, interlacing diffusions, mod-Ø convergence, Markov soup, stochastic billiards and other current streams of research.

A Lifetime Of Excursions Through Random Walks And L Vy Processes

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Author : Loïc Chaumont
language : en
Publisher: Springer Nature
Release Date : 2022-01-01

A Lifetime Of Excursions Through Random Walks And L Vy Processes written by Loïc Chaumont and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.

This collection honours Ron Doney’s work and includes invited articles by his collaborators and friends. After an introduction reviewing Ron Doney’s mathematical achievements and how they have influenced the field, the contributed papers cover both discrete-time processes, including random walks and variants thereof, and continuous-time processes, including Lévy processes and diffusions. A good number of the articles are focused on classical fluctuation theory and its ramifications, the area for which Ron Doney is best known.

In And Out Of Equilibrium 3 Celebrating Vladas Sidoravicius

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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.