The Dickman subordinator, renewal theorems, and disordered systems

Francesco Caravenna; Rongfeng Sun; Nikos Zygouras

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arXiv · 1805.01465

The Dickman subordinator, renewal theorems, and disordered systems

Francesco Caravenna·Rongfeng Sun·Nikos Zygouras

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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.

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Francesco Caravenna, Rongfeng Sun, Nikos Zygouras. 2018-05-03. The Dickman subordinator, renewal theorems, and disordered systems. https://arxiv.org/abs/1805.01465

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