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The Dickman subordinator, renewal theorems, and disordered systems
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Caravenna, Francesco, Sun, Rongfeng and Zygouras, Nikos (2019) The Dickman subordinator, renewal theorems, and disordered systems. Electronic Journal of Probability, 24 . 101. doi:10.1214/19-EJP353 ISSN 1083-6489.
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Official URL: https://doi.org/10.1214/19-EJP353
Abstract
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.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics T Technology > T Technology (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||||
Library of Congress Subject Headings (LCSH): | Lévy processes , Probabilities, Renewal theory, Chaotic behavior in systems -- Mathematics | ||||||||
Journal or Publication Title: | Electronic Journal of Probability | ||||||||
Publisher: | University of Washington. Dept. of Mathematics | ||||||||
ISSN: | 1083-6489 | ||||||||
Official Date: | 18 September 2019 | ||||||||
Dates: |
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Volume: | 24 | ||||||||
Article Number: | 101 | ||||||||
DOI: | 10.1214/19-EJP353 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | "The right to place the final version of this article (exactly as published in the journal) on their own homepage or in a public digital repository, provided there is a link to the official journal site." | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 9 September 2019 | ||||||||
Date of first compliant Open Access: | 26 September 2019 | ||||||||
RIOXX Funder/Project Grant: |
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