Upper bounds on the growth rate of Diffusion Limited Aggregation

2017/05/17 by Benjamini, Itai, Yadin, Ariel
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1705.06095

Abstract

We revisit Kesten's argument for the upper bound on the growth rate of DLA. We are able to make the argument robust enough so that it applies to many graphs, where only control of the heat kernel is required. We apply this to many examples including transitive graphs of polynomial growth, graphs of exponential growth, non-amenable graphs, super-critical percolation on Z^d, high dimensional pre-Sierpinski carpets. We also observe that a careful analysis shows that Kesten's original bound on Z³ can be improved from t^2/3 to (t log t)^1/2 .

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