Limit theorems for reinforced random walks on certain trees

Andrea Collevecchio

doi:10.1007/s00440-005-0476-x

Limit theorems for reinforced random walks on certain trees

Andrea Collevecchio

Research output: Contribution to journal › Article › Research › peer-review

12 Citations (Scopus)

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
Pages (from-to)	81-101
Number of pages	21
Journal	Probability Theory and Related Fields
Volume	136
Issue number	1
DOIs	https://doi.org/10.1007/s00440-005-0476-x
Publication status	Published - Sept 2006
Externally published	Yes

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AB - 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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Limit theorems for reinforced random walks on certain trees

Abstract

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