Large deviations for the chemical distance in supercritical Bernoulli percolation
| dc.creator | Garet, Olivier | |
| dc.creator | Marchand, Régine | |
| dc.date | 2004-09-18 | |
| dc.date | 2007-07-31 | |
| dc.date.accessioned | 2026-07-07T08:21:11Z | |
| dc.date.available | 2026-07-07T08:21:11Z | |
| dc.description | The chemical distance D(x,y) is the length of the shortest open path between two points x and y in an infinite Bernoulli percolation cluster. In this work, we study the asymptotic behaviour of this random metric, and we prove that, for an appropriate norm $μ$ depending on the dimension and the percolation parameter, the probability of the event \[\biggl\{0\leftrightarrow x,\frac{D(0,x)}{μ(x)}\notin (1-ε, 1+ε) \biggr\}\] exponentially decreases when $\|x\|_1$ tends to infinity. From this bound we also derive a large deviation inequality for the corresponding asymptotic shape result. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117906000000881 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/0409317 | |
| dc.identifier | http://arxiv.org/abs/math/0409317 | |
| dc.identifier | Annals of Probability 35, 3 (2007) 833-866 | |
| dc.identifier | doi:10.1214/009117906000000881 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135278 | |
| dc.subject | Probability | |
| dc.subject | 60K35 (Primary) 82B43 (Secondary) | |
| dc.title | Large deviations for the chemical distance in supercritical Bernoulli percolation | |
| dc.type | text |