Central moments of the free energy of the stationary O’Connell–Yor polymer

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-10-01 DOI:10.1214/21-aap1744

C. Noack, Philippe Sosoe

引用次数: 2

Abstract

Seppäläinen and Valkó showed in [20] that for a suitable choice of parameters, the variance growth of the free energy of the stationary O’Connell-Yor polymer is governed by the exponent 2/3, characteristic of models in the KPZ universality class. We develop exact formulas based on Gaussian integration by parts to relate the cumulants of the free energy, logZθ n,t, to expectations of products of quenched cumulants of the time of the first jump from the boundary into the system, s0. We then use these formulas to obtain estimates for the k-th central moment of logZθ n,t as well as the k-th annealed moment of s0 for k > 2, with nearly optimal exponents (1/3)k + and (2/3)k + , respectively. As an application, we derive new high probability bounds for the distance between the polymer path and a straight line connecting the origin to the endpoint of the path.

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静止O 'Connell-Yor聚合物自由能的中心矩

Seppäläinen和Valkó在[20]中表明，对于合适的参数选择，固定O’Connell-Yor聚合物的自由能的方差增长由指数2/3控制，这是KPZ普适性类模型的特征。我们开发了基于高斯逐部分积分的精确公式，以将自由能的累积量logZθn，t与从边界到系统的第一次跳跃时间s0的淬火累积量的乘积的期望值联系起来。然后，我们使用这些公式来获得logZθn，t的第k个中心矩以及s0的第k次退火矩的估计，当k>2时，分别具有近似最优的指数（1/3）k+和（2/3）k+。作为一个应用，我们推导了聚合物路径和连接路径起点和终点的直线之间距离的新的高概率界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.