Abstract
Consider a linearly edge-reinforced random walk defined on the b-ary tree, b≥70. We prove the strong law of large numbers for the distance of this process from the root. We give a sufficient condition for this strong law to hold for general edge-reinforced random walks and random walks in a random environment. We also provide a central limit theorem.
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Supported in part by a Purdue Research Foundation fellowship
this work is part of the author's PhD thesis.
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Collevecchio, A. Limit theorems for reinforced random walks on certain trees. Probab. Theory Relat. Fields 136, 81–101 (2006). https://doi.org/10.1007/s00440-005-0476-x
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DOI: https://doi.org/10.1007/s00440-005-0476-x