Longest increasing subsequence as expectation of a simple nonlinear   stochastic PDE with a low noise intensity
  We report some new observation concerning the statistics of Longest Increasing Subsequences (LIS). We show that the expectation of LIS, its variance, and apparently the full distribution function appears in statistical analysis of some simple nonlinear stochastic partial differential equation (SPDE) in the limit of very low noise intensity. 
E. Katzav, S. Nechaev, O. Vasilyev