On the scaling limit of simple random walk excursion measure in the plane

Details On the scaling limit of simple random walk excursion measure in the plane On the scaling limit of simple random walk excursion measure in the plane

2005-06-16

arxiv.org/abs/math/0506337v2

ALEA Lat. Am. J. Probab. Math. Stat., volume 2, paper 02-05, pages 125-155, 2006

Mathematics

Probability

v2: 31 pages, 0 figures; fixed minor typos, updated acknowledgements and references

Scientific paper

The Brownian excursion measure is a conformally invariant infinite measure on curves. It figured prominently in one of the first major applications of SLE, namely the explicit calculations of the planar Brownian intersection exponents from which the Hausdorff dimension of the frontier of the Brownian path could be computed (Lawler, Schramm, and Werner, 2001). In this paper we define the simple random walk excursion measure and show that for any bounded, simply connected Jordan domain D, the simple random walk excursion measure on D converges in the scaling limit to the Brownian excursion measure on D.

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