ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60J25,60K35 Granovsky Boris L. Spectral gap of certain continuous-time Markov processes. The talk is devoted to bounding the spectral gap of mean-field models and random walks on complete graphs. We study the behaviour of the spectral gap, as the number of sites N → ∞, and also as a function of the parameters of the process considered. Exact values of spectral gap are found in some cases. We also reveal a phenomenon of existence critical points of parameters w. r. t. spectral gap. The results are derived via extension of Zeifman’s method based on using the logarithmic norm of an operator.