Summary
This paper is devoted to the problem of the nearest, neighbour Random Walk on infinite graphs. We investigate the RW X n started from a fixed vertex X 0=x∈V of the graph G=(V, E) and the expected value of the first exit time T N from the N-ball B N in G. It will be shown that if G is sufficiently “regular” then
and
where d R is the RW dimension, d is the fractal dimension and d Ω is the exponent of the growth of the resistance of B N . Though the method of the paper was developed for the case when X 0=x is a fixed vertex of the graph, we hope that the result can be generalized.
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Telcs, A. Random Walks on graphs, electric networks and fractals. Probab. Th. Rel. Fields 82, 435–449 (1989). https://doi.org/10.1007/BF00339997
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DOI: https://doi.org/10.1007/BF00339997
Keywords
- Stochastic Process
- Fractal Dimension
- Random Walk
- Probability Theory
- Statistical Theory