An algebraic approach to scaling limits of up-down chains

Document Type

Presentation Abstract

Presentation Date

3-25-2024

Abstract

An up-down chain is a Markov chain in which each transition can be decomposed into a growth step followed by a reduction step. In general, these two steps can be unrelated, but if they satisfy a natural commutation relation, the up-down chain turns out to be particularly amenable to analysis.

In this talk, we will present a general framework for analyzing these special up-down chains. This approach will mainly be algebraic but will lead to convergence results. If time permits, we will discuss an example in the context of permutations and permutons.

Based on joint work with Valentin Féray.

Additional Details

March 25, 2024 at 3:00 p.m. Math 103

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