random-geometry

The scaling limit of Baxter permutations

Jacopo Borga / 2023-07-02

Versions of the following question can be traced back at least to the work of Henri Poincaré (Poincaré (1912)): In how many ways a simple loop in the plane can cross a line a specified number of times? Despite many efforts, this question remains open after more than a century. Let us start by…