Author : Thomas M. Liggett
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 12,87 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 3662039907
Interactive particle systems is a branch of probability theory with close connections to mathematical physics and mathematical biology. This book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. It explains and develops many of the most useful techniques in the field.
Author : T.M. Liggett
Publisher : Springer Science & Business Media
Page : 499 pages
File Size : 45,3 MB
Release : 2012-12-06
Category : Science
ISBN : 1461385423
At what point in the development of a new field should a book be written about it? This question is seldom easy to answer. In the case of interacting particle systems, important progress continues to be made at a substantial pace. A number of problems which are nearly as old as the subject itself remain open, and new problem areas continue to arise and develop. Thus one might argue that the time is not yet ripe for a book on this subject. On the other hand, this field is now about fifteen years old. Many important of several basic models is problems have been solved and the analysis almost complete. The papers written on this subject number in the hundreds. It has become increasingly difficult for newcomers to master the proliferating literature, and for workers in allied areas to make effective use of it. Thus I have concluded that this is an appropriate time to pause and take stock of the progress made to date. It is my hope that this book will not only provide a useful account of much of this progress, but that it will also help stimulate the future vigorous development of this field.
Author : Geoffrey Grimmett
Publisher : Cambridge University Press
Page : 279 pages
File Size : 15,29 MB
Release : 2018-01-25
Category : Mathematics
ISBN : 1108542999
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Author : Thomas Milton Liggett
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 23,49 MB
Release : 2010
Category : Mathematics
ISBN : 0821849492
Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.
Author : Nicolas Lanchier
Publisher : Walter de Gruyter GmbH & Co KG
Page : 651 pages
File Size : 33,31 MB
Release : 2024-07-01
Category : Mathematics
ISBN : 3110791935
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.
Author : Giambattista Giacomin
Publisher : Springer
Page : 654 pages
File Size : 49,12 MB
Release : 2019-06-30
Category : Mathematics
ISBN : 3030150968
Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas.
Author : Richard Courant
Publisher : Springer Science & Business Media
Page : 585 pages
File Size : 42,13 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642571492
From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991
Author : Rick Durrett
Publisher : Cambridge University Press
Page : 203 pages
File Size : 41,81 MB
Release : 2010-05-31
Category : Mathematics
ISBN : 1139460889
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Author : Richard Durrett
Publisher : Wadsworth Publishing Company
Page : 352 pages
File Size : 44,86 MB
Release : 1988
Category : Science
ISBN :
Author : Claude Kipnis
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 47,75 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 3662037521
This book has been long awaited in the "interacting particle systems" community. Begun by Claude Kipnis before his untimely death, it was completed by Claudio Landim, his most brilliant student and collaborator. It presents the techniques used in the proof of the hydrodynamic behavior of interacting particle systems.
