Random Walks On Disordered Media And Their Scaling Limits

Author : Takashi Kumagai
Publisher : Springer
Page : 147 pages
File Size : 40,8 Mb
Release : 2014-01-25
Category : Mathematics
ISBN : 9783319031521

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Random Walks on Disordered Media and their Scaling Limits by Takashi Kumagai Pdf

In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster(‘the ant in the labyrinth’)is one of the typical examples. In 1986, H. Kesten showed the anomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.

Author : Takashi Kumagai
Publisher : Unknown
Page : 162 pages
File Size : 52,8 Mb
Release : 2014-02-28
Category : Electronic
ISBN : 3319031538

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Random Walks on Disordered Media and Their Scaling Limits by Takashi Kumagai Pdf

Author : V. Sidoravicius,S. Smirnov
Publisher : American Mathematical Soc.
Page : 471 pages
File Size : 54,8 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.

Author : Kazuo Nishimura,Masatoshi Murase,Kazuyoshi Yoshimura
Publisher : Springer Nature
Page : 427 pages
File Size : 54,9 Mb
Release : 2021-10-26
Category : Business & Economics
ISBN : 9789811644573

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Creative Complex Systems by Kazuo Nishimura,Masatoshi Murase,Kazuyoshi Yoshimura Pdf

In recent years, problems such as environmental and economic crises and pandemics caused by new viruses have been occurring on a global scale. Globalization brings about benefits, but it can increase the potential risks of “systemic problems”, leading to system-wide disruptions. The coronavirus pandemic, declared on March 11, 2020, by the World Health Organization, has revealed social disparities in the form of a higher risk of death for people of low-socioeconomic status and has caused massive destruction of the economy and of globalization itself. Extensive efforts to cope with these challenges have often led to the emergence of additional problems due to the chain of hidden causation. What can be done to protect against such emerging challenges? Despite the resulting complexity, once these individual problems are considered as different aspects of a single whole, seemingly contradictory issues can become totally understandable, as they can be integrated into a single coherent framework. This is the integrationist approach in contrast to the reductionist approach. Situations of this kind are truly relevant to understanding the question, “What are creative complex systems?” This book features contributions by members and colleagues of the Kyoto University International Research Unit of Integrated Complex System Science. It broadens our outlook from the traditional view of stability, in which global situations are eventually stabilized after the impact of destruction, to “creative” complex systems.

Author : M. T. Barlow
Publisher : Cambridge University Press
Page : 239 pages
File Size : 51,8 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9781107674424

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Random Walks and Heat Kernels on Graphs by M. T. Barlow Pdf

Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.

Author : Franco Flandoli
Publisher : Springer
Page : 182 pages
File Size : 42,8 Mb
Release : 2011-03-02
Category : Mathematics
ISBN : 9783642182310

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Random Perturbation of PDEs and Fluid Dynamic Models by Franco Flandoli Pdf

The book deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices.

Author : Patricia Alonso Ruiz,Michael Hinz,Kasso A. Okoudjou,Luke G. Rogers,Alexander Teplyaev
Publisher : Springer Nature
Page : 294 pages
File Size : 49,5 Mb
Release : 2023-11-25
Category : Mathematics
ISBN : 9783031378003

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From Classical Analysis to Analysis on Fractals by Patricia Alonso Ruiz,Michael Hinz,Kasso A. Okoudjou,Luke G. Rogers,Alexander Teplyaev Pdf

Over the course of his distinguished career, Robert Strichartz (1943-2021) had a substantial impact on the field of analysis with his deep, original results in classical harmonic, functional, and spectral analysis, and in the newly developed analysis on fractals. This is the first volume of a tribute to his work and legacy, featuring chapters that reflect his mathematical interests, written by his colleagues and friends. An introductory chapter summarizes his broad and varied mathematical work and highlights his profound contributions as a mathematical mentor. The remaining articles are grouped into three sections – functional and harmonic analysis on Euclidean spaces, analysis on manifolds, and analysis on fractals – and explore Strichartz’ contributions to these areas, as well as some of the latest developments.

Author : Alain-Sol Sznitman
Publisher : European Mathematical Society
Page : 128 pages
File Size : 47,9 Mb
Release : 2012
Category : Gaussian processes
ISBN : 3037191090

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Topics in Occupation Times and Gaussian Free Fields by Alain-Sol Sznitman Pdf

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.

Author : Martin T. Barlow,Gordon Slade
Publisher : Springer Nature
Page : 421 pages
File Size : 51,8 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.

Author : Alexander Grigor'yan,Yuhua Sun
Publisher : Walter de Gruyter GmbH & Co KG
Page : 526 pages
File Size : 54,9 Mb
Release : 2021-01-18
Category : Mathematics
ISBN : 9783110700763

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Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs by Alexander Grigor'yan,Yuhua Sun Pdf

The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.

Author : Zhen-Qing Chen,Takashi Kumagai,Jian Wang
Publisher : American Mathematical Society
Page : 89 pages
File Size : 47,8 Mb
Release : 2021-09-24
Category : Mathematics
ISBN : 9781470448639

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Stability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms by Zhen-Qing Chen,Takashi Kumagai,Jian Wang Pdf

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Author : Pierluigi Contucci,Cristian Giardinà
Publisher : Cambridge University Press
Page : 383 pages
File Size : 40,5 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.

Author : B.D. Hughes,B.W. Ninham
Publisher : Springer
Page : 438 pages
File Size : 51,7 Mb
Release : 2006-11-14
Category : Science
ISBN : 9783540386933

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The Mathematics and Physics of Disordered Media by B.D. Hughes,B.W. Ninham Pdf

Author : Uta Freiberg,Ben Hambly,Michael Hinz,Steffen Winter
Publisher : Springer Nature
Page : 307 pages
File Size : 42,7 Mb
Release : 2021-03-23
Category : Mathematics
ISBN : 9783030596491

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Fractal Geometry and Stochastics VI by Uta Freiberg,Ben Hambly,Michael Hinz,Steffen Winter Pdf

This collection of contributions originates from the well-established conference series "Fractal Geometry and Stochastics" which brings together researchers from different fields using concepts and methods from fractal geometry. Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, self-similar trees, p-hyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemi-stable distributions and fractional differential equations, and diffusion limited aggregation. Representing a rich source of ideas and a good starting point for more advanced topics in fractal geometry, the volume will appeal to both established experts and newcomers.

Author : Tadahisa Funaki,Wojbor Woyczynski
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384687

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Nonlinear Stochastic PDEs by Tadahisa Funaki,Wojbor Woyczynski Pdf

This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability." We thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations was held during the week of March 21 at the Institute for Mathematics and Its Applications at the University of Minnesota. It was part of the Special Year on Emerging Applications of Probability program put together by an organizing committee chaired by J. Michael Steele. The selection of topics reflected personal interests of the organizers with two areas of emphasis: the hydrodynamic limit problems and Burgers' turbulence and related models. The talks and the papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.