Aaron Smith

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math.PR2013

Comparison Theory for Markov Chains on Different State Spaces and Application to Random Walk on Derangements

Aaron Smith

Let $X_{t}$ and $Y_{t}$ be two Markov chains, on state spaces $Ω \subset Ω^$ . In this paper, we discuss how to prove bounds on the spectrum of $X_{t}$ based on bounds on the spec…

math.PR2012

The Cutoff Phenomenon for Random Birth and Death Chains

Aaron Smith

For any distribution $π$ with support equal to $[n] = {1, 2, ..., n}$ , we study the set $A_{π}$ of tridiagonal stochastic matrices $K$ satisfying $π(i) K[i,j] = π(j) K[j,…