Kelvin Rivera-Lopez (Gonzawa University)
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ECE 026
An up-down chain is a Markov chain in which each transition can be decomposed into a growth step followed by a reduction step. Generally, these two steps are unrelated, but when they satisfy a natural commutation relation, the up-down chain is particularly amenable to analysis. For example, one can describe the spectrum of the transition matrix and often analyze convergence rates.
In the first part of this talk, we will discuss some new results concerning these special up-down chains. Topics include eigenvectors and diffusive limits. Afterwards, we will discuss a new family of permutons and its associated up-down chain on permutations.
Based on joint work with Valentin Féray.