From Markov Chains to Non-Equilibrium Particle Systems
From Markov Chains to Non-Equilibrium Particle Systems
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DOI：
10.1142/1389
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发表时间：
1992-03
期刊：
影响因子：
--
通讯作者：
Mu-Fa Chen
中科院分区：
文献类型：
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作者：
Mu-Fa Chen
本卷介绍了中国probabilists的概率论及其在物理学中的应用的代表性工作。有趣的跳跃马尔可夫过程的结果进行了讨论，以及马尔可夫相互作用过程与非紧状态，包括Schlogal模型从统计物理。这本书的主体是独立的，可以在随机过程的研究生课程中使用。本书由四部分组成。在第一、二部分中，作者介绍了跳过程的一般理论。对经典问题的新贡献：唯一性、常返性和正常返性进行了研究。然后讨论了概率度量和耦合方法、随机单调性、可逆性、大偏差和L平方谱间隙的估计。第三部分从研究平衡粒子系统开始。这包括可逆性的判据、吉布斯态的构造和格点分形上的粒子系统。最后一部分着重讨论了反应扩散过程，这是由非平衡态统计物理学产生的。主题包括构造、定态分布的存在性、遍历性、相变和过程的流体动力学极限。
This volume presents a representative work of Chinese probabilists on probability theory and its applications in physics. Interesting results of jump Markov processes are discussed, as well as Markov interacting processes with noncompact states, including the Schlogal model taken from statistical physics. The main body of this book is self-contained and can be used in a course in stochastic processes for graduate students. The book consists of four parts. In Parts 1 and 2, the author introduces the general theory for jump processes. New contributions to the classical problems: uniqueness, recurrence and positive recurrence are studied. Then, probability metrics and coupling methods, stochastically monotonicity, reversibility, large deviations and the estimates of L squared-spectral gap are discussed. Part 3 begins with the study of equilibrium particle systems. This contains the criteria of the reversibility, the construction of Gibbs states and the particle systems on lattice fractals. The final part emphasizes the reaction-diffusion processes which come from non-equilibrium statistical physics. Topics include constructions, existence of stationary distributions, ergodicity, phase transitions and hydrodynamic limits for the processes.