Limit theorems for reinforced random walks on certain trees

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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 languageEnglish
Pages (from-to)81-101
Number of pages21
JournalProbability Theory and Related Fields
Volume136
Issue number1
DOIs
Publication statusPublished - Sep 2006
Externally publishedYes

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