Speaker: Erik Slivken, Paris VII

Date and time: Thursday, September 27, 4-5pm

Place: Phillips 110

Title: The local limit of the fixed-point forest

Abstract: We begin with a simple sorting algorithm on a randomly ordered stack of cards labeled 1 through *n*. If the first card is labeled *k*, slide that card into the *k*th position. Repeat until the first card is a 1. This algorithm induces a directed forest structure on the set of permutations. The local limit of this structure converges to a random tree which itself can be constructed directly from a sequence of Poisson point processes. We are able to compute a variety of statistics related to this tree, such as the distribution of the longest and shortest path to a leaf, or its expected size. We also study generalizations of this random tree.

## When

Thu, September 27, 2018

4:00 p.m. - 5:00 p.m.

## Where

Phillips Hall

Room: 110