Asymptotic behavior of eigenvalues and random updating schemes

For a stochastic matrix (Q_ij^T)_i,j=1^M withQ_ij^T exp(–U(ij)/T) at the off-diagonal positions, we develop an algorithm to evaluate the asymptotic convergence rate of all eigenvalues ofQ_ij^T asT 0 using Ventcel's optimal graphs. As an application we can compare the convergence rates of some random updating schemes used in image processing.This research was partially supported by the National Science Council, Taiwan and Air Force Office of Scientific Research Contract No. F49620 S5C 0144, and was completed while Tzuu-Shuh Chiang was visiting the Center for Stochastic Processes, Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260, USA.