FIRST-PASSAGE PERCOLATION ON CARTESIAN POWER GRAPHS
Artikel i vetenskaplig tidskrift, 2018

We consider first-passage percolation on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product G square G square...square G of some base graph G as the number of factors tends to infinity. We propose a natural asymptotic lower bound on the first-passage time between (v, v,...,v) and (w, w,...,w) as n, the number of factors, tends to infinity, which we call the critical time t(G)*(v,w). Our main result characterizes when this lower bound is sharp as n ->infinity. As a corollary, we are able to determine the limit of the so-called diagonal time-constant in Z(n) as n ->infinity for a large class of distributions of passage times.

high dimension

power graph

hypercube

time constant

First-passage percolation

Författare

Anders Martinsson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

Annals of Probability

0091-1798 (ISSN)

Vol. 46 2 1004-1041

Ämneskategorier

Reglerteknik

Diskret matematik

Matematisk analys

DOI

10.1214/17-AOP1199

Mer information

Senast uppdaterat

2018-05-21