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February 2015 Tails of the endpoint distribution of directed polymers
Jeremy Quastel, Daniel Remenik
Ann. Inst. H. Poincaré Probab. Statist. 51(1): 1-17 (February 2015). DOI: 10.1214/12-AIHP525

Abstract

We prove that the random variable $\mathcal{T}=\operatorname{arg\,max}_{t\in\mathbb{R}}\{\mathcal{A}_{2}(t)-t^{2}\}$, where $\mathcal{A}_{2}$ is the $\mathrm{Airy}_{2}$ process, has tails which decay like $\mathrm{e}^{-ct^{3}}$. The distribution of $\mathcal{T}$ is a universal distribution which governs the rescaled endpoint of directed polymers in $1+1$ dimensions for large time or temperature.

Nous prouvons qu’une variable aléatoire $\mathcal{T}=\operatorname{arg\,max}_{t\in\mathbb{R}}\{\mathcal{A}_{2}(t)-t^{2}\}$, où $\mathcal{A}_{2}$ est un processus $\mathrm{Airy}_{2}$ a une queue qui décroît comme $\mathrm{e}^{-ct^{3}}$. La distribution de $\mathcal{T}$ est une distribution universelle qui gouverne la position du point final d’un polymère dirigé en dimension $1+1$ à temps grand ou à grande température.

Citation

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Jeremy Quastel. Daniel Remenik. "Tails of the endpoint distribution of directed polymers." Ann. Inst. H. Poincaré Probab. Statist. 51 (1) 1 - 17, February 2015. https://doi.org/10.1214/12-AIHP525

Information

Published: February 2015
First available in Project Euclid: 14 January 2015

zbMATH: 1314.60159
MathSciNet: MR3300961
Digital Object Identifier: 10.1214/12-AIHP525

Subjects:
Primary: 60K35, 82C23

Rights: Copyright © 2015 Institut Henri Poincaré

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Vol.51 • No. 1 • February 2015
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