The Dickman subordinator, renewal theorems, and disordered systems

被引：12

作者：

Caravenna, Francesco ^{[1
]}

Sun, Rongfeng ^{[2
]}

Zygouras, Nikos ^{[3
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 55, I-20125 Milan, Italy

[2] Natl Univ Singapore, Dept Math, 10 Lower Kent Ridge Rd, Singapore 119076, Singapore

[3] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2019年 / 24卷

基金：

英国工程与自然科学研究理事会;

关键词：

Dickman subordinator; Dickman function; renewal process; Levy process; renewal theorem; stable process; disordered system; pinning model; directed polymer model; SUMS;

D O I：

10.1214/19-EJP353

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the so-called Dickman subordinator, whose Levy measure has density 1/x restricted to the interval (0, 1). The marginal density of this process, known as the Dickman function, appears in many areas of mathematics, from number theory to combinatorics. In this paper, we study renewal processes in the domain of attraction of the Dickman subordinator, for which we prove local renewal theorems. We then present applications to marginally relevant disordered systems, such as pinning and directed polymer models, and prove sharp second moment estimates on their partition functions.

引用

页数：40

共 34 条

[1] THE INTERMEDIATE DISORDER REGIME FOR DIRECTED POLYMERS IN DIMENSION 1+1 [J].