Capacitive flows on a 2D random net
| dc.creator | Garet, Olivier | |
| dc.date | 2006-08-28 | |
| dc.date | 2009-05-14 | |
| dc.date.accessioned | 2026-07-07T13:14:35Z | |
| dc.date.available | 2026-07-07T13:14:35Z | |
| dc.description | This paper concerns maximal flows on $\mathbb{Z}^2$ traveling from a convex set to infinity, the flows being restricted by a random capacity. For every compact convex set $A$, we prove that the maximal flow $Φ(nA)$ between $nA$ and infinity is such that $Φ(nA)/n$ almost surely converges to the integral of a deterministic function over the boundary of $A$. The limit can also be interpreted as the optimum of a deterministic continuous max-flow problem. We derive some properties of the infinite cluster in supercritical Bernoulli percolation. | |
| dc.description | 20 pages, 1 figure published in The Annals of Applied Probability http://www.imstat.org/aap/ | |
| dc.identifier | https://arxiv.org/abs/math/0608676 | |
| dc.identifier | http://arxiv.org/abs/math/0608676 | |
| dc.identifier | The Annals of Applied Probability 19, 2 (2009) 641 | |
| dc.identifier | doi:10.1214/08-AAP556 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230253 | |
| dc.subject | Probability | |
| dc.subject | 60K35, 82B43 | |
| dc.title | Capacitive flows on a 2D random net | |
| dc.type | text |