Upper bounds on the growth rate of Diffusion Limited Aggregation

Understand

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} .