Random Walks On Disordered Media And Their Scaling Limits PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Random Walks On Disordered Media And Their Scaling Limits PDF full book. Access full book title Random Walks On Disordered Media And Their Scaling Limits.
Author | : Takashi Kumagai |
Publisher | : Springer |
Total Pages | : 155 |
Release | : 2014-01-25 |
Genre | : Mathematics |
ISBN | : 331903152X |
Download Random Walks on Disordered Media and their Scaling Limits Book in PDF, ePub and Kindle
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 | : |
Total Pages | : 162 |
Release | : 2014-02-28 |
Genre | : |
ISBN | : 9783319031538 |
Download Random Walks on Disordered Media and Their Scaling Limits Book in PDF, ePub and Kindle
Author | : V. Sidoravicius |
Publisher | : American Mathematical Soc. |
Total Pages | : 482 |
Release | : 2016-04-28 |
Genre | : Mathematics |
ISBN | : 1470422484 |
Download Probability and Statistical Physics in St. Petersburg Book in PDF, ePub and Kindle
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 |
Publisher | : Springer Nature |
Total Pages | : 427 |
Release | : 2021-10-26 |
Genre | : Business & Economics |
ISBN | : 9811644578 |
Download Creative Complex Systems Book in PDF, ePub and Kindle
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 | : Franco Flandoli |
Publisher | : Springer |
Total Pages | : 187 |
Release | : 2011-03-02 |
Genre | : Mathematics |
ISBN | : 3642182313 |
Download Random Perturbation of PDEs and Fluid Dynamic Models Book in PDF, ePub and Kindle
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 |
Publisher | : Springer Nature |
Total Pages | : 294 |
Release | : 2023-11-25 |
Genre | : Mathematics |
ISBN | : 3031378008 |
Download From Classical Analysis to Analysis on Fractals Book in PDF, ePub and Kindle
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 |
Total Pages | : 128 |
Release | : 2012 |
Genre | : Gaussian processes |
ISBN | : 9783037191095 |
Download Topics in Occupation Times and Gaussian Free Fields Book in PDF, ePub and Kindle
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 |
Publisher | : Springer Nature |
Total Pages | : 421 |
Release | : 2019-12-03 |
Genre | : Mathematics |
ISBN | : 3030320111 |
Download Random Graphs, Phase Transitions, and the Gaussian Free Field Book in PDF, ePub and Kindle
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 |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 526 |
Release | : 2021-01-18 |
Genre | : Mathematics |
ISBN | : 311070076X |
Download Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs Book in PDF, ePub and Kindle
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 |
Publisher | : American Mathematical Society |
Total Pages | : 89 |
Release | : 2021-09-24 |
Genre | : Mathematics |
ISBN | : 1470448637 |
Download Stability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms Book in PDF, ePub and Kindle
View the abstract.