Optimal flow through the disordered lattice

Details Optimal flow through the disordered lattice Optimal flow through the disordered lattice

2005-11-29

arxiv.org/abs/math/0511694v2

Annals of Probability 2007, Vol. 35, No. 2, 397-438

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000719 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000719

Consider routing traffic on the N x N torus, simultaneously between all source-destination pairs, to minimize the cost $\sum_ec(e)f^2(e)$, where f(e) is the volume of flow across edge e and the c(e) form an i.i.d. random environment. We prove existence of a rescaled $N\to \infty$ limit constant for minimum cost, by comparison with an appropriate analogous problem about minimum-cost flows across a M x M subsquare of the lattice.

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