From Markov Chains To Non-equilibrium Particle Systems (2nd Edition)

From Markov Chains To Non-equilibrium Particle Systems (2nd Edition) PDF

Author: Mu-fa Chen

Publisher: World Scientific

Published: 2004-03-23

Total Pages: 610

ISBN-13: 9814482900

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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.

From Markov Chains to Non-equilibrium Particle Systems

From Markov Chains to Non-equilibrium Particle Systems PDF

Author: Mufa Chen

Publisher: World Scientific

Published: 2004

Total Pages: 610

ISBN-13: 9812388117

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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.

Probability and Phase Transition

Probability and Phase Transition PDF

Author: G.R. Grimmett

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 334

ISBN-13: 9401583269

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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.

Non-Dissipative Effects in Nonequilibrium Systems

Non-Dissipative Effects in Nonequilibrium Systems PDF

Author: Christian Maes

Publisher: Springer

Published: 2017-09-20

Total Pages: 53

ISBN-13: 3319677802

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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.

Stochastic Interacting Systems: Contact, Voter and Exclusion Processes

Stochastic Interacting Systems: Contact, Voter and Exclusion Processes PDF

Author: Thomas M. Liggett

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 346

ISBN-13: 3662039907

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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.

Scaling Limits of Interacting Particle Systems

Scaling Limits of Interacting Particle Systems PDF

Author: Claude Kipnis

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 453

ISBN-13: 3662037521

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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.

Eigenvalues, Inequalities, and Ergodic Theory

Eigenvalues, Inequalities, and Ergodic Theory PDF

Author: Mu-Fa Chen

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 239

ISBN-13: 1846281237

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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

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