The Metastable Behavior of the Three Dimensional Ising Model

The problem of metastability has attracted a great attention in the recent decade.In particular, it has been extensively investigated the 2-dimensional Ising model ina finite torus [CFQ]、[NS]、[Sch]. In this paper, the 3-dimensional Ising model withGlauber dynamics under a positive magnetic field is considered. We characterize themetastable behavior in the pathwise approacb, find out all metastable states, anddetermine naturally the critical droplet. We give a general and clear view of the sub-stance of the passage from all spins down (- 1) to all spins up (+ 1). For a largeclass of initial states, the logarithmic asymptotics of the hitting time of - 1 or + 1 areaccurately estimated, and the shrink and growth of droplets are described.     

ON THE STATISTICAL MECHANICS OF PROBABILISTIC MODELS OF NEURAL NETWORKS

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一族带指数扰动的Markov链的亚稳态性(Ⅰ)

考虑有限状态空间上一可约Markov链及其指数扰动的不可约Markov链族,这是Freidlin-Wentzell理论的推广,首先是出于随机Ising模型、神经网络、模拟退火等方面的考虑,现证明一大类Markov链族都有亚稳态性,亚稳态就是可约Markov链的常返类,还仔细分析了高阶吸引子、高阶吸引域及其金字塔形结构,估计不同集合首达时的渐近指数量阶,首达时间除其平均值之后收敛到均值为1的指数分布.     

MINIMAL COUPLED DIFFUSION PROCESS

An attempt is made to classify the boundary of the coupled operator Ω(Ω=(?)Ω_i=d/(dx)a_i(x)d/(dx)+b_i(x)d/(dx),i=1,2)and to construct the corresponding minimalsemigroup and minimal coupled diffusion process.The sample properties and tho conservativeconditions of the process are discussed also.     

贝努里学会第一届世界大会情况简介

今年九月八日至十四日在苏联塔什干市举行了贝努里学会第一届世界大会.来自世界近五十个国家的一千名代表(其中包括五百名左右苏联代表及五百名左右来自世界其它各国的代表)参加了大会.三名中国概率统计学者参加了会议,他们是:中国科技大学的苏淳与北京大学的谢衷洁与钱敏平.大会于九月八日上午举行开幕式,由苏联Proholov主持,开幕式后由Kolmogorov与Uspensky作了“随机性与算法”的报告.继而,大会分四个会场,对35个专题进行.每个专题一般有2—3个特邀报告与5个交流报告,其它报告以张贴形式交流. 由于这次大会代表的广泛,论题方向的全面以及大会的精心组织和妥善安排使得这次大会不仅是一次极好的世界性交流机会,也是一次世界概率统计发展动态与方向的大展示.为     

连续时间参数马氏链的环流与某些行列式的概率意义

本文讨论了连续时间参数的马氏链的不可逆性与环流的关系,用计算行列式方法建立了文献[1]中的概率方法与Hill结果的联系。     

ON DONSKER AND VARADHAN''''S ASYMPTOTIC EVALUATION WITHOUT COMPACTNESS

Donsker and Varadhan have developed in a series of papers [1—3] a newtechnique to estimate the rate of exponential decay for certain probabilities associatedwith occupation times for Markov processes.We wish to investigate to what extentthe compactness condition is actually necessary.As a first step,we consider here thefollowing question.Let X be a metric space and let dx be a measure on X.Let C(X)be the space ofbounded continuous functions on X and p_t be a strongly continuous semigroup such     

Metastability of Exponentially Perturbed Markov Chains

Motivated by studies of the stochastic Ising models at very low temperature,neural networks and simulating annealing, we consider a family of Markov chains asa perturbation of another Markov chain. The main theme of this paper is to demon-strate that the metastable behavior happens universally for this wide class of process.Assume the state space X = {ξ,η,…} is finite, and the transition matrices P~β =     

一族带指数扰动的Markov链的亚稳态性(Ⅱ)

分析了高阶吸引子与高阶吸引域及其金字塔形的结构,估计不同集合首达时的渐近指数阶,首达时间除以其平均值后收敛至参数为1的指数分布.     

Rd上的具有间断梯度的势函数的模拟退火

证明了具有间断梯度的势函数的模拟退火过程 dX_t=-β(tÑU(X_t)+√2dW_t 依概率收敛到势函数的全局最小点附近.