Exact Rates of Convergence for Some Non-reversible Markov Chains
refreshments at 3:45pm
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
Speaker's Contact Info: elizabeth.wilmer(at-sign)oberlin.edu
Return to seminar home page
Page loaded on May 08, 2000 at 11:05 AM.
Copyright © 1998-99, Sara C. Billey.
All rights reserved.