{TALK
{"May 12}
{"Exact Rates of Convergence for Some Non-reversible Markov Chains}
{"Elizabeth Wilmer}
{"Oberlin College}
{"elizabeth.wilmer@oberlin.edu}
{"
While extensive work has been done bounding rates of convergence of
symmetric and/or reversible Markov chains, less is known about the
convergence behavior of arbitrary non-reversible chains. We give detailed
descriptions of the long-term behavior of some simple families of
non-reversible chains; these families have many deterministic transitions
and underlying graphs ``close'' to a one-way cycle. We obtain local limit
theorems for the distributions of these chains prior to stationarity. In
all cases considered, the time to arrive at a fixed distance from
stationarity is asymptotically O(n^3/m(n)), where n is the total number of
states and m(n) is the number of states with more than one possible
successor.
}
}