Tails of the endpoint distribution of directed polymers

Details Tails of the endpoint distribution of directed polymers Tails of the endpoint distribution of directed polymers

2012-03-13

arxiv.org/abs/1203.2907v2

Mathematics

Probability

16 pages, 1 figure

Scientific paper

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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