Abstract
We consider linearly edge-reinforced random walk on an arbitrary locally finite connected graph. It is shown that the process has the same distribution as a mixture of reversible Markov chains, determined by time-independent strictly positive weights on the edges. Furthermore, we prove bounds for the random weights, uniform, among others, in the size of the graph.
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Merkl, F., Rolles, S.W.W. A random environment for linearly edge-reinforced random walks on infinite graphs. Probab. Theory Relat. Fields 138, 157–176 (2007). https://doi.org/10.1007/s00440-006-0016-3
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DOI: https://doi.org/10.1007/s00440-006-0016-3
Keywords
- Reinforced random walk
- Random environment
Mathematics Subject Classifications (2000)
- Primary 60K35
- Secondary 60K37