Limit theorems for maximum flows on a lattice

Details Limit theorems for maximum flows on a lattice Limit theorems for maximum flows on a lattice

2007-10-24

arxiv.org/abs/0710.4589v3

Mathematics

Probability

57 pages, 6 figures

Scientific paper

We independently assign a non-negative value, as a capacity for the quantity of flows per unit time, with a distribution F to each edge on the Z^d lattice. We consider the maximum flows through the edges of two disjoint sets, that is from a source to a sink, in a large cube. In this paper, we show that the ratio of the maximum flow and the size of source is asymptotic to a constant. This constant is denoted by the flow constant.

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