Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity

TL;DR

This paper links the statistics of Longest Increasing Subsequences to the behavior of a simple nonlinear stochastic PDE in the low noise limit, revealing new statistical insights.

Contribution

It demonstrates that the expectation, variance, and distribution of LIS can be derived from a specific nonlinear SPDE at low noise levels, a novel connection.

Findings

LIS statistics relate to a nonlinear SPDE in low noise limit

Expectation and variance of LIS are derived from the SPDE

Distribution function of LIS appears in the SPDE analysis

Abstract

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.