Longest increasing subsequence as expectation of a simple nonlinear stochastic partial differential equation with a low noise intensity.
We report some observations concerning the statistics of longest increasing subsequences (LIS). We argue 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 in the limit of very low noise intensity.
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, CNRS UMR 8550, 24 rue Lhomond, 75231 Paris Cedex 05, France.
E
E
Katzav
S
S
Nechaev
O
O
Vasilyev