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arXiv · 1203.2907

Tails of the endpoint distribution of directed polymers

Jeremy Quastel·Daniel Remenik
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Abstract

We prove that the random variable $\ct=\argmax_{t\in\rr}\{\aip(t)-t^2\}$ has tails which decay like $e^{-ct^3}$. 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.

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Jeremy Quastel, Daniel Remenik. 2012-03-13. Tails of the endpoint distribution of directed polymers. https://doi.org/10.1214/12-aihp525

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