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.
Original language | English |
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Pages (from-to) | 81-101 |
Number of pages | 21 |
Journal | Probability Theory and Related Fields |
Volume | 136 |
Issue number | 1 |
DOIs | |
Publication status | Published - Sep 2006 |
Externally published | Yes |