Optimal flow through the disordered lattice

• 成果类型: Article
• 署名作者: Aldous, David
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000719
• 发表日期: 2007
• 页码: 397-438
• 关键词: maximal flows; percolation

摘要

Consider routing traffic on the N x N torus, simultaneously between all source-destination pairs, to minimize the cost Sigma e c(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 -> infinity 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.