Tails of the endpoint distribution of directed polymers
  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. 
Jeremy Quastel and Daniel Remenik
math.PR math-ph math.MP