One step replica symmetry breaking and extreme order statistics of logarithmic REMs

Author:

Cao Xiangyu123,Fyodorov Yan4,Le Doussal Pierre15

Affiliation:

1. French National Centre for Scientific Research

2. University of Paris-Saclay

3. University of Paris-Sud

4. King's College London

5. École Normale Supérieure

Abstract

Building upon the one-step replica symmetry breaking formalism, we show that the extreme values of a general class of Euclidean-space logarithmic correlated random energy models behave as a randomly shifted decorated exponential Poisson point process in the thermodynamic limit. The distribution of the random shift is determined solely by the large-distance ( “infra-red”, IR) limit of the model, and is equal to the free energy distribution at the critical temperature up to a translation. the decoration process is determined solely by the small-distance (“ultraviolet”, UV) limit, in terms of the biased minimal process. We discuss the relations of our approach with that based on the freezing/duality conjecture, and connections to results in the probability literature. Our approach allowed us to derive the general and explicit formulae for the joint probability density of depths of the first and second minima (as well its higher-order generalizations) in terms of model-specific contributions from UV as well as IR limits. In particular, we show that the distribution of the second minimum is independent of UV data, and depends on IR behaviour via a single parameter, the mean value of the gap. For a given log-correlated field this parameter can be evaluated numerically, and we provide several numerical tests of our theory using the circular model of 1/f-noise.

Funder

Engineering and Physical Sciences Research Council

National Science Foundation

Publisher

Stichting SciPost

Subject

General Physics and Astronomy

Cited by 11 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3