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We report some new observation concerning the statistics of LongestIncreasing Subsequences (LIS). We show that the expectation of LIS, itsvariance, and apparently the full distribution function appears in statisticalanalysis of some simple nonlinear stochastic partial differential equation(SPDE) in the limit of very low noise intensity.

Longest increasing subsequence as expectation of a simple nonlinear stochastic partial differential equation with a low noise intensity