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Universality for conformally invariant intersection exponents

Gregory Lawler;  Wendelin Werner — 2000

Journal of the European Mathematical Society

We construct a class of conformally invariant measures on sets (or paths) and we study the critical exponents called intersection exponents associated to these measures. We show that these exponents exist and that they correspond to intersection exponents between planar Brownian motions. More precisely, using the definitions and results of our paper [27], we show that any set defined under such a conformal invariant measure behaves exactly as a pack (containing maybe a non-integer number) of Brownian...

A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions

Gregory F. Lawler — 2010

ESAIM: Probability and Statistics

The growth exponent for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius is of order . We prove that in two dimensions, the growth exponent is strictly greater than one. The proof uses a known estimate on the third moment of the escape probability and an improvement on the discrete Beurling projection theorem.

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