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Edge-reinforced random walk on finite graphs. (English) Zbl 0986.05092

Clément, Ph. (ed.) et al., Infinite dimensional stochastic analysis. Proceedings of the colloquium, Amsterdam, Netherlands, February 11-12, 1999. Amsterdam: Royal Netherlands Academy of Arts and Sciences. Verh. Afd. Natuurkd., 1. Reeks, K. Ned. Akad. Wet. 52, 217-234 (2000).
Summary: We consider reinforced random walk, in which the transition probabilities at each step are influenced by the number of crossings of the edges. For finite graphs we prove a limit theorem for the joint distribution of the normalized occupation time of the edges and the normalized cycle numbers (number of times the random walk winds around the individual cycles of the graph). The limiting distribution is calculated explicitely.
For the entire collection see [Zbl 0968.00044].

MSC:

05C80 Random graphs (graph-theoretic aspects)
60G50 Sums of independent random variables; random walks
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