Upper bounds on the growth rate of Diffusion Limited Aggregation

Itai Benjamini, Ariel Yadin

Research output: Working paper/PreprintPreprint

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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 Z^3 can be improved from t^{2/3} to (t log t)^{1/2} .
Original languageEnglish GB
PublisherarXiv:1705.06095 [math.PR]
StatePublished - 1 May 2017

Keywords

  • Mathematics - Probability
  • Mathematical Physics

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