A lower bound on the growth exponent for loop-erased random walk in two dimensions
A Lower Bound on the Growth Exponent for Loop-Erased Random Walk in Two Dimensions
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.
Values of brownian intersection exponents III : two-sided exponents
Strict concavity of the half plane intersection exponent for planar Brownian motion.
Nonintersecting planar Brownian motions.
Hausdorff dimension of cut points for Brownian motion.
Cut times for simple random walk.
Strict concavity of the intersection exponent for Brownian motion in two and three dimensions.
Loop-erased walks intersect infinitely often in four dimensions.
The Beurling estimate for a class of random walks.
Estimates of random walk exit probabilities and application to loop-erased random walk.
Geometric interpretation of half-plane capacity.
One-arm exponent for critical 2D percolation.
Irreducible compositions and the first return to the origin of a random walk.
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