A random environment for linearly edge-reinforced random walks on infinite graphs |
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| Authors: | Franz Merkl Silke W. W. Rolles |
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| Affiliation: | 1. Mathematical Institute, University of Munich, Theresienstr. 39, 80333, Munich, Germany
2. Zentrum Mathematik, Bereich M5, Technische Universit?t München, 85747, Garching bei München, Germany
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| 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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| Keywords: | Reinforced random walk Random environment |
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