The Contact Process On A Finite Set Ii

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The Contact Process On A Finite Set Ii

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Author : Richard Durrett
language : en
Publisher:
Release Date : 1987

The Contact Process On A Finite Set Ii written by Richard Durrett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.

The Contact Process On A Finite Set Iii

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Author : Richard Durrett
language : en
Publisher:
Release Date : 1988

The Contact Process On A Finite Set Iii written by Richard Durrett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.

Stochastic Interacting Systems Contact Voter And Exclusion Processes

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Author : Thomas M. Liggett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Stochastic Interacting Systems Contact Voter And Exclusion Processes written by Thomas M. Liggett 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 2013-03-09 with Mathematics categories.

Interactive Particle Systems is a branch of Probability Theory with close connections to Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T. Liggett, Interacting Particle System, ISBN 3-540-96069) that treated the subject as it was at that time. The present book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. In so doing, many of the most useful techniques in the field are explained and developed, so that they can be applied to other models and in other contexts. Extensive Notes and References sections discuss other work on these and related models. Readers are expected to be familiar with analysis and probability at the graduate level, but it is not assumed that they have mastered the material in the 1985 book. This book is intended for graduate students and researchers in Probability Theory, and in related areas of Mathematics, Biology and Physics.

The Contact Process 1974 1989

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Author : Richard Durrett
language : en
Publisher:
Release Date : 1989

The Contact Process 1974 1989 written by Richard Durrett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Birth and death processes (Stochastic processes) categories.

Mathematics Of Random Media

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Author : Werner E. Kohler
language : en
Publisher: American Mathematical Soc.
Release Date :

Mathematics Of Random Media written by Werner E. Kohler 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 with Mathematics categories.

In recent years, there has been remarkable growth in the mathematics of random media. The field has deep scientific and technological roots, as well as purely mathematical ones in the theory of stochastic processes. This collection of papers by leading researchers provides an overview of this rapidly developing field. The papers were presented at the 1989 AMS-SIAM Summer Seminar in Applied Mathematics, held at Virginia Polytechnic Institute and State University in Blacksburg, Virginia. In addition to new results on stochastic differential equations and Markov processes, fields whose elegant mathematical techniques are of continuing value in application areas, the conference was organized around four themes: Systems of interacting particles are normally viewed in connection with the fundamental problems of statistical mechanics, but have also been used to model diverse phenomena such as computer architectures and the spread of biological populations. Powerful mathematical techniques have been developed for their analysis, and a number of important systems are now well understood. Random perturbations of dynamical systems have also been used extensively as models in physics, chemistry, biology, and engineering. Among the recent unifying mathematical developments is the theory of large deviations, which enables the accurate calculation of the probabilities of rare events. For these problems, approaches based on effective but formal perturbation techniques parallel rigorous mathematical approaches from probability theory and partial differential equations. The book includes representative papers from forefront research of both types. Effective medium theory, otherwise known as the mathematical theory of homogenization, consists of techniques for predicting the macroscopic properties of materials from an understanding of their microstructures. For example, this theory is fundamental in the science of composites, where it is used for theoretical determination of electrical and mechanical properties. Furthermore, the inverse problem is potentially of great technological importance in the design of composite materials which have been optimized for some specific use. Mathematical theories of the propagation of waves in random media have been used to understand phenomena as diverse as the twinkling of stars, the corruption of data in geophysical exploration, and the quantum mechanics of disordered solids. Especially effective methods now exist for waves in randomly stratified, one-dimensional media. A unifying theme is the mathematical phenomenon of localization, which occurs when a wave propogating into a random medium is attenuated exponentially with propagation distance, with the attenuation caused solely by the mechanism of random multiple scattering. Because of the wide applicability of this field of research, this book would appeal to mathematicians, scientists, and engineers in a wide variety of areas, including probabilistic methods, the theory of disordered materials, systems of interacting particles, the design of materials, and dynamical systems driven by noise. In addition, graduate students and others will find this book useful as an overview of current research in random media.

Phase Transitions Of Interacting Particle Systems

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Author : Norio Konno
language : en
Publisher: World Scientific
Release Date : 1995-01-16

Phase Transitions Of Interacting Particle Systems written by Norio Konno and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-16 with Mathematics categories.

Recently, interacting particle systems have been studied widely from the standpoints of mathematics, physics, chemistry and biology. Many researchers are becoming interested in this field.This book focuses on the phase transitions of interacting particle systems, especially their critical values and order parameters. It poses the following question: How can we get good bounds on the critical values and the order parameters? This question is very basic, and many researchers have been trying to get better bounds rigorously. Hence the book provides bounds — both the author's and others'.

Probability And Phase Transition

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Author : G.R. Grimmett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Probability And Phase Transition written by G.R. Grimmett 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 2013-04-17 with Science categories.

This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability. The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.

Large Deviations And Metastability

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Author : Enzo Olivieri
language : en
Publisher: Cambridge University Press
Release Date : 2005-02-21

Large Deviations And Metastability written by Enzo Olivieri 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 2005-02-21 with Mathematics categories.

The book provides a general introduction to the theory of large deviations and a wide overview of the metastable behaviour of stochastic dynamics. With only minimal prerequisites, the book covers all the main results and brings the reader to the most recent developments. Particular emphasis is given to the fundamental Freidlin-Wentzell results on small random perturbations of dynamical systems. Metastability is first described on physical grounds, following which more rigorous approaches to its description are developed. Many relevant examples are considered from the point of view of the so-called pathwise approach. The first part of the book develops the relevant tools including the theory of large deviations which are then used to provide a physically relevant dynamical description of metastability. Written to be accessible to graduate students, this book provides an excellent route into contemporary research.

Perplexing Problems In Probability

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Author : Maury Bramson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Perplexing Problems In Probability written by Maury Bramson 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 2012-12-06 with Mathematics categories.

Harry Kesten has had a profound influence on probability theory for over 30 years. To honour his achievements a number of prominent probabilists have written survey articles on a wide variety of active areas of contemporary probability, many of which are closely related to Kesten's work.

Stochastic Interacting Systems In Life And Social Sciences

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Author : Nicolas Lanchier
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-07-01

Stochastic Interacting Systems In Life And Social Sciences written by Nicolas Lanchier and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-01 with Mathematics categories.

This volume provides an overview of two of the most important examples of interacting particle systems, the contact process, and the voter model, as well as their many variants introduced in the past 50 years. These stochastic processes are organized by domains of application (epidemiology, population dynamics, ecology, genetics, sociology, econophysics, game theory) along with a flavor of the mathematical techniques developed for their analysis.