Download or read book From Markov Chains To Non equilibrium Particle Systems 2nd Edition written by Mu-fa Chen and published by World Scientific. This book was released on 2004-03-23 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is representative of the work of Chinese probabilists on probability theory and its applications in physics. It presents a unique treatment of general Markov jump processes: uniqueness, various types of ergodicity, Markovian couplings, reversibility, spectral gap, etc. It also deals with a typical class of non-equilibrium particle systems, including the typical Schlögl model taken from statistical physics. The constructions, ergodicity and phase transitions for this class of Markov interacting particle systems, namely, reaction-diffusion processes, are presented. In this new edition, a large part of the text has been updated and two-and-a-half chapters have been rewritten. The book is self-contained and can be used in a course on stochastic processes for graduate students.
Download or read book From Markov Chains to Non equilibrium Particle Systems written by Mu Fa Chen and published by . This book was released on 1994 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book From Markov Chains to Non equilibrium Particle Systems written by Mu Fa Chen and published by . This book was released on 1992 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book From Markov Chains to Non equilibrium Particle Systems written by Mufa Chen and published by World Scientific. This book was released on 2004 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is representative of the work of Chinese probabilists on probability theory and its applications in physics. It presents a unique treatment of general Markov jump processes: uniqueness, various types of ergodicity, Markovian couplings, reversibility, spectral gap, etc. It also deals with a typical class of non-equilibrium particle systems, including the typical Schlögl model taken from statistical physics. The constructions, ergodicity and phase transitions for this class of Markov interacting particle systems, namely, reaction-diffusion processes, are presented. In this new edition, a large part of the text has been updated and two-and-a-half chapters have been rewritten. The book is self-contained and can be used in a course on stochastic processes for graduate students.
Download or read book Aspects of Markov Chains and Particle Systems written by Shirshendu Ganguly and published by . This book was released on 2016 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thesis concerns asymptotic behavior of particle systems and the underlying Markov chains used to model various natural phenomena. The objective is to describe and analyze stochastic models involving spatial structure and evolution over time. Fundamental objects of interest in such systems include the equilibrium measure which the system converges to, the phenomenon of phase transition in the long term behavior and the time taken to converge to stationarity. In this thesis we present three examples highlighting the above aspects. In Chapter 2, we will discuss Competitive Erosion: a multi-particle system introduced by James Propp in 2003, as a generalization of a fundamental growth model known as Internal Diffusion Limited Aggregation. In this model, each vertex of the graph is occupied by a particle, which can be either red or blue. New red and blue particles are emitted alternately from their respective bases and perform random walk. On encountering a particle of the opposite color they remove it and occupy its position. We consider competitive erosion on discretizations of smooth planar simply connected domains. In Chapter 2 we establish positively, a conjecture of Propp regarding conformal invariance of the the model at stationarity, by showing that, with high probability the blue and the red regions are separated by an orthogonal circular arc on the disc and by a suitable hyperbolic geodesic on a general `smooth' simply connected domain. In Chapter 3, we discuss a family of conservative stochastic processes known as Activated Random Walk (ARW) which interpolates between ordinary random walk and the Stochastic Sandpile; the latter being a canonical example of Self Organized Criticality. These processes are conjectured to exhibit a sharp change in long time behavior depending on the value of certain parameters. Informally ARW is a particle system on Z with mass conservation. One starts with a mass density mu>0 of initially active particles, each of which performs a symmetric random walk at rate one and falls asleep at rate lambda. Sleepy particles become active on coming in contact with other active particles. We investigate the question of fixation/non-fixation of the process and show for small enough lambda, the critical mass density for fixation is strictly less than one. Moreover, the critical density goes to zero as lambda tends to zero. This positively answers two open questions from Dickman, Rolla, Sidoravicius (J. Stat. Phys., 2010) and Rolla, Sidoravicius (Invent. Math., 2012). In Chapter 4, we discuss a model of constrained Glauber dynamics, known as the East Process, exhibiting sharp convergence to equilibrium. The East process is a 1-D kinetically constrained interacting particle system, introduced in the physics literature in the early 90's to model liquid-glass transitions. Informally, it is a two spin (0,1) system on Z, where every site at rate one tries to randomize its spin using a fresh Bernoulli (p). However the move is suppressed unless the site to the left is in the 0 state. Thus the Glauber dynamics move is carried out only in the presence of a certain `kinetic' constraint. Spectral gap estimates of Aldous and Diaconis in 2002 imply that its mixing time on L sites has order L. Since the relaxation time is of a smaller order than the mixing time it is natural to expect a sharp convergence to equilibrium . Proving this, is the goal of this chapter, where we establish Cutoff for mixing, with an optimal window size.
Download or read book Statistical Physics II written by R. Kubo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of Statistical Physics consititutes the second part of Statistical Physics (Springer Series in Solid-State Science, Vols. 30, 31) and is devoted to nonequilibrium theories of statistical mechanics. We start with an intro duction to the stochastic treatment of Brownian motion and then proceed to general problems involved in deriving a physical process from an underlying more basic process. Relaxation from nonequilibrium to equilibrium states and the response of a system to an external disturbance form the central problems of nonequilibrium statistical mechanics. These problems are treated both phenomenologically and microscopically along the lines of re cent developments. Emphasis is placed on fundamental concepts and methods rather than on applications which are too numerous to be treated exhaustively within the limited space of this volume. For information on the general aim of this book, the reader is referred to the Foreword. For further reading, the reader should consult the bibliographies, although these are not meant to be exhaustive.
Download or read book Probability and Phase Transition written by G.R. Grimmett and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Additive and Cancellative Interacting Particle Systems written by D. Griffeath and published by Springer. This book was released on 2006-11-15 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non Dissipative Effects in Nonequilibrium Systems written by Christian Maes and published by Springer. This book was released on 2017-09-20 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces and discusses both the fundamental aspects and the measurability of applications of time-symmetric kinetic quantities, outlining the features that constitute the non-dissipative branch of non-equilibrium physics. These specific features of non-equilibrium dynamics have largely been ignored in standard statistical mechanics texts. This introductory-level book offers novel material that does not take the traditional line of extending standard thermodynamics to the irreversible domain. It shows that although stationary dissipation is essentially equivalent with steady non-equilibrium and ubiquitous in complex phenomena, non-equilibrium is not determined solely by the time-antisymmetric sector of energy-entropy considerations. While this should not be very surprising, this book provides timely, simple reminders of the role of time-symmetric and kinetic aspects in the construction of non-equilibrium statistical mechanics.
Download or read book Stochastic Interacting Systems Contact Voter and Exclusion Processes written by Thomas M. Liggett and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scaling Limits of Interacting Particle Systems written by Claude Kipnis and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Eigenvalues Inequalities and Ergodic Theory written by Mu-Fa Chen and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first and only book to make this research available in the West Concise and accessible: proofs and other technical matters are kept to a minimum to help the non-specialist Each chapter is self-contained to make the book easy-to-use
Download or read book Interacting Particle Systems written by T.M. Liggett and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book From Markov Chains to Nonequlibrium Particle Systems written by Mu Fa Chen and published by . This book was released on 1992 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Genealogies Of Interacting Particle Systems written by Matthias Birkner and published by World Scientific. This book was released on 2020-02-24 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interacting particle systems are Markov processes involving infinitely many interacting components. Since their introduction in the 1970s, researchers have found many applications in statistical physics and population biology. Genealogies, which follow the origin of the state of a site backwards in time, play an important role in their studies, especially for the biologically motivated systems.The program Genealogies of Interacting Particle Systems held at the Institute for Mathematical Sciences, National University of Singapore, from 17 July to 18 Aug 2017, brought together experts and young researchers interested in this modern topic. Central to the program were learning sessions where lecturers presented work outside of their own research, as well as a normal workshop. This is reflected in the present volume which contains two types of articles:Written by respected researchers, including experts in the field such as Steve Evans, member of the US National Academy of Sciences, as well as Anton Wakolbinger, Andreas Greven, and many others, this volume will no doubt be a valuable contribution to the probability community.
Download or read book Measure Valued Branching Markov Processes written by Zenghu Li and published by Springer Nature. This book was released on 2023-04-14 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a compact introduction to the theory of measure-valued branching processes, immigration processes and Ornstein–Uhlenbeck type processes. Measure-valued branching processes arise as high density limits of branching particle systems. The first part of the book gives an analytic construction of a special class of such processes, the Dawson–Watanabe superprocesses, which includes the finite-dimensional continuous-state branching process as an example. Under natural assumptions, it is shown that the superprocesses have Borel right realizations. Transformations are then used to derive the existence and regularity of several different forms of the superprocesses. This technique simplifies the constructions and gives useful new perspectives. Martingale problems of superprocesses are discussed under Feller type assumptions. The second part investigates immigration structures associated with the measure-valued branching processes. The structures are formulated by skew convolution semigroups, which are characterized in terms of infinitely divisible probability entrance laws. A theory of stochastic equations for one-dimensional continuous-state branching processes with or without immigration is developed, which plays a key role in the construction of measure flows of those processes. The third part of the book studies a class of Ornstein-Uhlenbeck type processes in Hilbert spaces defined by generalized Mehler semigroups, which arise naturally in fluctuation limit theorems of the immigration superprocesses. This volume is aimed at researchers in measure-valued processes, branching processes, stochastic analysis, biological and genetic models, and graduate students in probability theory and stochastic processes.
Download or read book Continuous Time Markov Decision Processes written by Alexey Piunovskiy and published by Springer Nature. This book was released on 2020-11-09 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic and rigorous treatment of continuous-time Markov decision processes, covering both theory and possible applications to queueing systems, epidemiology, finance, and other fields. Unlike most books on the subject, much attention is paid to problems with functional constraints and the realizability of strategies. Three major methods of investigations are presented, based on dynamic programming, linear programming, and reduction to discrete-time problems. Although the main focus is on models with total (discounted or undiscounted) cost criteria, models with average cost criteria and with impulsive controls are also discussed in depth. The book is self-contained. A separate chapter is devoted to Markov pure jump processes and the appendices collect the requisite background on real analysis and applied probability. All the statements in the main text are proved in detail. Researchers and graduate students in applied probability, operational research, statistics and engineering will find this monograph interesting, useful and valuable.
