## Combinatorics Seminar

When: Sunday, November 15, 10am
Where: Schreiber 309
Speaker: Richard Kenyon, Brown University
Title: A variational principle for permutations
## Abstract:

We study scaling limits of large permutations ("permutons"),
constrained by fixing certain of pattern densities, for example,
the density of inversions or `123' patterns. We show that the limit
shapes are determined by maximizing entropy over permutons with
those constraints. In particular, we compute (exactly or numerically)
the limit shapes with fixed 12 density, with fixed 12 and 123
densities, with fixed 12 density and the sum of 123 and 213 densities.
In some cases one can find interesting phase transitions as one varies
the densities.
To obtain our results, we also provide a description of permutons
using a dynamic construction.
This is joint work with Daniel Kráľ, Charles Radin and Pete
Winkler.