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 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 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 1999-08-13 with total page 356 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. 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.
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 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 Nonlinear Analysis Geometry and Applications written by Diaraf Seck and published by Springer Nature. This book was released on 2020-11-20 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24–28, 2019. The four-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems. The book addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal transportation, control theory, and mathematical modeling.
Download or read book Modeling Stochastic Control Optimization and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.
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 Dirichlet Forms and Related Topics written by Zhen-Qing Chen and published by Springer Nature. This book was released on 2022-09-04 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference proceeding contains 27 peer-reviewed invited papers from leading experts as well as young researchers all over the world in the related fields that Professor Fukushima has made important contributions to. These 27 papers cover a wide range of topics in probability theory, ranging from Dirichlet form theory, Markov processes, heat kernel estimates, entropy on Wiener spaces, analysis on fractal spaces, random spanning tree and Poissonian loop ensemble, random Riemannian geometry, SLE, space-time partial differential equations of higher order, infinite particle systems, Dyson model, functional inequalities, branching process, to machine learning and Hermitizable problems for complex matrices. Researchers and graduate students interested in these areas will find this book appealing.
Download or read book New Directions in Function Theory From Complex to Hypercomplex to Non Commutative written by Daniel Alpay and published by Springer Nature. This book was released on 2022-01-01 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory. The papers, written by leading researchers in the field, relate to hypercomplex analysis, Schur analysis and de Branges spaces, new aspects of classical function theory, and infinite dimensional analysis. Signal processing constitutes a strong presence in several of the papers.A second volume in this series of conferences, this book will appeal to mathematicians interested in learning about new fields of development in function theory.
Download or read book From Particle Systems to Partial Differential Equations written by Patrícia Gonçalves and published by Springer. This book was released on 2017-11-15 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the dynamic Ö4 theory in three space dimensions, as well as selected contributions presented at the fourth meeting on Particle Systems and PDEs, which was held at the University of Minho’s Centre of Mathematics in December 2015. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, offering them a forum to present their recent results and discuss their topics of expertise. The meeting was also intended to present to a vast and varied public, including young researchers, the area of interacting particle systems, its underlying motivation, and its relation to partial differential equations. The book will be of great interest to probabilists, analysts, and all mathematicians whose work focuses on topics in mathematical physics, stochastic processes and differential equations in general, as well as physicists working in statistical mechanics and kinetic theory.”
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 On the Duality Relation Between Interacting Particle Systems and Markov Chains written by Anja Voß-Böhme and published by . This book was released on 2009 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
