Values of Brownian intersection exponents III: Two-sided exponents

Gregory F. Lawler; Oded Schramm; Wendelin Werner

doi:10.1016/S0246-0203(01)01089-5

paper

Values of Brownian intersection exponents III: Two-sided exponents

arXiv:math/0005294 · doi:10.1016/S0246-0203(01)01089-5

Abstract

This paper determines values of intersection exponents between packs of planar Brownian motions in the half-plane and in the plane that were not derived in our first two papers. For instance, it is proven that the exponent $ξ (3, 3)$ describing the asymptotic decay of the probability of non-intersection between two packs of three independent planar Brownian motions each is $(73 - 273) /12$ . More generally, the values of $ξ (w_{1}, > ..., w_{k})$ and $\tx (w_1', ..., w_k')$ are determined for all $k \geq 2$ , $w_{1}, w_{2} \geq 1$ , $w_{3}, ..., w_{k} \in [0, \infty)$ and all $w_{1}^{'}, ..., w_{k}^{'} \in [0, \infty)$ . The proof relies on the results derived in our first two papers and applies the same general methods. We first find the two-sided exponents for the stochastic Loewner evolution processes in a half-plane, from which the Brownian intersection exponents are determined via a universality argument.

Values of Brownian intersection exponents III: Two-sided exponents

Abstract

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