On the transience of processes defined on Galton--Watson trees
| dc.creator | Collevecchio, Andrea | |
| dc.date | 2006-06-29 | |
| dc.date.accessioned | 2026-07-07T07:17:50Z | |
| dc.date.available | 2026-07-07T07:17:50Z | |
| dc.description | We introduce a simple technique for proving the transience of certain processes defined on the random tree $\mathcal{G}$ generated by a supercritical branching process. We prove the transience for once-reinforced random walks on $\mathcal{G}$, that is, a generalization of a result of Durrett, Kesten and Limic [Probab. Theory Related Fields 122 (2002) 567--592]. Moreover, we give a new proof for the transience of a family of biased random walks defined on $\mathcal{G}$. Other proofs of this fact can be found in [Ann. Probab. 16 (1988) 1229--1241] and [Ann. Probab. 18 (1990) 931--958] as part of more general results. A similar technique is applied to a vertex-reinforced jump process. A by-product of our result is that this process is transient on the 3-ary tree. Davis and Volkov [Probab. Theory Related Fields 128 (2004) 42--62] proved that a vertex-reinforced jump process defined on the $b$-ary tree is transient if $b\ge 4$ and recurrent if $b=1$. The case $b=2$ is still open. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117905000000837 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0606751 | |
| dc.identifier | http://arxiv.org/abs/math/0606751 | |
| dc.identifier | Annals of Probability 2006, Vol. 34, No. 3, 870-878 | |
| dc.identifier | doi:10.1214/009117905000000837 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114087 | |
| dc.subject | Probability | |
| dc.subject | 60G50, 60J80 (Primary) 60J75 (Secondary) | |
| dc.title | On the transience of processes defined on Galton--Watson trees | |
| dc.type | text |