The length of the longest increasing subsequence in the Brownian separable permutons

Vienna Probability Seminar

The Brownian separable permutons are a family of universal limits of random constrained permutations, depending on some parameter p in (0,1). We prove explicit polynomial bounds for the length of the longest increasing subsequence in the Brownian separable permutons, and present simulations suggesting that the lower bound is close to optimal for all p. The strategy relies on a connection to fragmentation processes that I will highlight in the talk. The talk is based on joint work with Jacopo Borga (Stanford University) and Ewain Gwynne (University of Chicago).