静止O 'Connell-Yor聚合物自由能的中心矩

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2022-10-01 DOI:10.1214/21-aap1744

C. Noack, Philippe Sosoe

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引用次数: 2

摘要

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。

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

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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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.