论文信息 - On the time taken by random walks on finite groups to visit every state

On the time taken by random walks on finite groups to visit every state

SummaryConsider a random walk on a finite group G. Suppose that the time taken for the transition probabilities to approach the uniform distribution is small compared with #G. Then the time taken for the random walk to visit every state is approximately R#G·log(#G), where R is the mean number of returns to the initial state in the short term.

D. Aldous

[1] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1967 .

[2] W. Feller,et al. An Introduction to Probability Theory and Its Applications, Vol. 1 , 1967 .

[3] D. Aldous. Markov chains with almost exponential hitting times , 1982 .

[4] D. Aldous. Random walks on finite groups and rapidly mixing markov chains , 1983 .

[5] D. Aldous. Minimization Algorithms and Random Walk on the $d$-Cube , 1983 .