00559238

j

00559238 Lynch, James F. Threshold functions for Markov chains: A graph theoretic approach. Comb. Probab. Comput. 2, No.3, 351-362 (1993). 1993 Cambridge University Press, Cambridge EN Markov chains with variable transition stationary distribution

doi:10.1017/S0963548300000729

The author studies finite state Markov chains with variable transition probabilities $P(\varepsilon)= [p\sb{ij}(\varepsilon)]$ depending on a small parameter $\varepsilon$. By using the methods of random graph theory, he obtains a new proof of convergence of $P(\varepsilon)\sp t$ to a stationary distribution as $\varepsilon\to 0$. Here $t= t(\varepsilon)$ is a function satisfying certain growth conditions. A new algorithm for computing the limit distributions is given. Z.Vondra\v{c}ek (Saarbr\"ucken)