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July, 1988 Phase Transition in Reinforced Random Walk and RWRE on Trees
Robin Pemantle
Ann. Probab. 16(3): 1229-1241 (July, 1988). DOI: 10.1214/aop/1176991687


A random walk on an infinite tree is given a particular kind of positive feedback so edges already traversed are more likely to be traversed in the future. Using exchangeability theory, the process is shown to be equivalent to a random walk in a random environment (RWRE), that is to say, a mixture of Markov chains. Criteria are given to determine whether a RWRE is transient or recurrent. These criteria apply to show that the reinforced random walk can vary from transient to recurrent, depending on the value of an adjustable parameter measuring the strength of the feedback. The value of the parameter at the phase transition is calculated.


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Robin Pemantle. "Phase Transition in Reinforced Random Walk and RWRE on Trees." Ann. Probab. 16 (3) 1229 - 1241, July, 1988.


Published: July, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0648.60077
MathSciNet: MR942765
Digital Object Identifier: 10.1214/aop/1176991687

Primary: 60J15
Secondary: 60J80

Keywords: mixture of Markov chains , Polya urn , random walk on trees , Reinforced random walk

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 3 • July, 1988
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