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.

Caravenna, F., Sun, R., Zygouras, N. (2019). The dickman subordinator, renewal theorems, and disordered systems. ELECTRONIC JOURNAL OF PROBABILITY, 24, 1-40 [10.1214/19-EJP353].

The dickman subordinator, renewal theorems, and disordered systems

Caravenna F.;
2019

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.
Articolo in rivista - Articolo scientifico
Dickman function; Dickman subordinator; Directed polymer model; Disordered system; Levy process; Pinning model; Renewal process; Renewal theorem; Stable process
English
2019
24
1
40
101
none
Caravenna, F., Sun, R., Zygouras, N. (2019). The dickman subordinator, renewal theorems, and disordered systems. ELECTRONIC JOURNAL OF PROBABILITY, 24, 1-40 [10.1214/19-EJP353].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/247848
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