1203.2907 (Jeremy Quastel et al.)

Tails of the endpoint distribution of directed polymers    [PDF]

Jeremy Quastel, Daniel Remenik

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.

View original: http://arxiv.org/abs/1203.2907