Exact Rates of Convergence for Some Nonreversible Markov Chains
Elizabeth Wilmer
Oberlin College
May 12,
4:15pm
refreshments at 3:45pm
2338
ABSTRACT

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 nonreversible chains. We give detailed
descriptions of the longterm behavior of some simple families of
nonreversible chains; these families have many deterministic transitions
and underlying graphs ``close'' to a oneway 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.

Speaker's Contact Info: elizabeth.wilmer(atsign)oberlin.edu
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