Abstract
This paper concerns maximal flows on ℤ2 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.
Citation
Olivier Garet. "Capacitive flows on a 2D random net." Ann. Appl. Probab. 19 (2) 641 - 660, April 2009. https://doi.org/10.1214/08-AAP556
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