Open Access
March 2007 Optimal flow through the disordered lattice
David Aldous
Ann. Probab. 35(2): 397-438 (March 2007). DOI: 10.1214/009117906000000719


Consider routing traffic on the N×N torus, simultaneously between all source-destination pairs, to minimize the cost ∑ec(e)f2(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→∞ limit constant for minimum cost, by comparison with an appropriate analogous problem about minimum-cost flows across a M×M subsquare of the lattice.


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David Aldous. "Optimal flow through the disordered lattice." Ann. Probab. 35 (2) 397 - 438, March 2007.


Published: March 2007
First available in Project Euclid: 30 March 2007

zbMATH: 1154.90003
MathSciNet: MR2308584
Digital Object Identifier: 10.1214/009117906000000719

Primary: 90B15
Secondary: 60K37

Keywords: concentration of measure , Disordered lattice , first passage percolation , flow , Local weak convergence , random network , routing

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 2 • March 2007
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