Translator Disclaimer
2019 The Dickman subordinator, renewal theorems, and disordered systems
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
Electron. J. Probab. 24: 1-40 (2019). DOI: 10.1214/19-EJP353

Abstract

We consider the so-called Dickman subordinator, whose Lévy measure has density $\frac{1} {x}$ 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.

Citation

Download Citation

Francesco Caravenna. Rongfeng Sun. Nikos Zygouras. "The Dickman subordinator, renewal theorems, and disordered systems." Electron. J. Probab. 24 1 - 40, 2019. https://doi.org/10.1214/19-EJP353

Information

Received: 22 October 2018; Accepted: 10 August 2019; Published: 2019
First available in Project Euclid: 18 September 2019

zbMATH: 07107385
MathSciNet: MR4017119
Digital Object Identifier: 10.1214/19-EJP353

Subjects:
Primary: 60K05
Secondary: 60G51, 82B44

JOURNAL ARTICLE
40 PAGES


SHARE
Vol.24 • 2019
Back to Top