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Stable limit laws for randomly biased walks on supercritical trees

Abstract:

We consider a random walk on a supercritical Galton-Watson tree with leaves, where the transition probabilities of the walk are determined by biases that are randomly assigned to the edges of the tree. The biases are chosen independently on distinct edges, each one according to a given law that satisfies a logarithmic non-lattice condition. We determine the condition under which the walk is sub-ballistic, and, in the sub-ballistic regime, we find a formula for the exponent gamma (which is pos...

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Publication status:
Published

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Publisher copy:
10.1214/12-A0P752

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Institution:
University of Oxford
Department:
Oxford, MPLS, Statistics
Journal:
ANNALS OF PROBABILITY
Volume:
41
Issue:
3A
Pages:
1694-1766
Publication date:
2011-01-20
DOI:
ISSN:
0091-1798
URN:
uuid:6e1f8220-0cae-471f-aebe-2c94f770d574
Source identifiers:
204296
Local pid:
pubs:204296
Language:
English
Keywords:

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