随机Ising转移矩阵乘积的Lyapunov指数：平衡无序情形

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Alea-Latin American Journal of Probability and Mathematical Statistics Pub Date : 2021-04-30 DOI:10.30757/ALEA.v19-27

G. Giacomin, R. L. Greenblatt

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引用次数: 1

摘要

我们分析了几种无序统计力学模型分析中出现的2 × 2矩阵序列乘积的上李雅普诺夫指数:例如，这些矩阵是具有随机外场的最近邻伊辛链的传递矩阵，而这个伊辛链的自由能密度就是我们所考虑的李雅普诺夫指数。当外场为中心时，我们得到了该指数在大相互作用极限下的尖锐行为:这种平衡情况在许多方面都是至关重要的。从数学的角度，我们精确地确定了一个接近于上下李雅普诺夫指数重合的对角随机矩阵的二维随机矩阵的乘积的上李雅普诺夫指数的行为。特别是,李雅普诺夫指数只是\ log - h \“老美元连续的。

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Lyapunov exponent for products of random Ising transfer matrices: the balanced disorder case

We analyze the top Lyapunov exponent of the product of sequences of two by two matrices that appears in the analysis of several statistical mechanics models with disorder: for example these matrices are the transfer matrices for the nearest neighbor Ising chain with random external field, and the free energy density of this Ising chain is the Lyapunov exponent we consider. We obtain the sharp behavior of this exponent in the large interaction limit when the external field is centered: this balanced case turns out to be critical in many respects. From a mathematical standpoint we precisely identify the behavior of the top Lyapunov exponent of a product of two dimensional random matrices close to a diagonal random matrix for which top and bottom Lyapunov exponents coincide. In particular, the Lyapunov exponent is only $\log$-H\"older continuous.

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来源期刊

Alea-Latin American Journal of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

期刊介绍： ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.