- 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...
Expand abstract - Publication status:
- Published
- Publisher copy:
- 10.1214/12-A0P752
-
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- 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:
- Copyright date:
- 2011
- Notes:
-
85 pages, seven figures. Sections 2.3 and 2.4 have been substantially
rewritten, and a glossary of notation has been introduced. To appear in Ann.
Probab., with the arXiv version containing a more extensive discussion of
relationships with other models in Sections 1.9 and 1.10
Journal article
Stable limit laws for randomly biased walks on supercritical trees
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