Samenvatting
We consider a transient random walk (X n ) in random environment on a Galton–Watson tree. Under fairly general assumptions, we give a sharp and explicit criterion for the asymptotic speed to be positive. As a consequence, situations with zero speed are revealed to occur. In such cases, we prove that X n is of order of magnitude n ¿, with . We also show that the linearly edge reinforced random walk on a regular tree always has a positive asymptotic speed, which improves a recent result of Collevecchio (Probab Theory Related 136(1):81–101, 2006).
Originele taal-2 | Engels |
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Pagina's (van-tot) | 525-559 |
Tijdschrift | Probability Theory and Related Fields |
Volume | 142 |
Nummer van het tijdschrift | 3-4 |
DOI's | |
Status | Gepubliceerd - 2008 |