Tomer Zimhoni, Ben Gurion University
"Random Permutations from Free Products"
Consider a random permutation on N elements denoted by A, which is drawn uniformly from the collection {σ ∈ SN | σ3 = id}. Additionally, let B be another random permutation, uniformly selected from the set {σ ∈ SN | σ2 = id}. Let γ be a word in A and B; for instance, γ could be represented as ABAAB. This way γ defines a new random permutation, given by choosing A and B and then take the composition A◦B◦A◦A◦B. In the forthcoming talk, we will discuss several results regarding the distribution of such a γ-random permutation as N grows to infinity, such as calculating the limit of the expected number of fixed points of a γ-random permutation. We show a surprising relation between such outcomes to topological and algebraic invariants of elements in free products of groups. This talk is based on my joint work with Doron Puder from Tel Aviv University.
This seminar will be held both online and in person:
- Room: MC 5479
- Zoom link: https://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09