Tails of the endpoint distribution of directed polymers

Abstract

We prove that the random variable $\ct=\argmax_{t\in\rr}\{\aip(t)-t^2\}$ has tails which decay like $e^{-c{t}^3}$. The distribution of $\ct$ is a universal distribution which governs the rescaled endpoint of directed polymers in 1+1 dimensions for large time or temperature.

To appear in Annales de l'Institut Henri Poincaré Probabilités et Statistiques (17 pages, 1 figure)

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Cited by in corpus (10)

• The KPZ equation with flat initial condition and the directed polymer with one free end
• Extremes of N vicious walkers for large N: application to the directed polymer and KPZ interfaces
• Airy processes and variational problems
• Reunion probability of N vicious walkers: typical and large fluctuations for large N
• On the joint distribution of the maximum and its position of the Airy2 process minus a parabola
• TASEP on a ring in sub-relaxation time scale
• Multiplicative functionals on ensembles of non-intersecting paths
• Stochastic growth in time dependent environments
• Painleve II in random matrix theory and related fields
• Localization and free energy asymptotics in disordered statistical mechanics and random growth models