Values of Brownian intersection exponents III: Two-sided exponents

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 xi(3, 3) describing the asymptotic decay of the probability of non-intersection between two packs of three independent planar Brownian motions each is (73-2root73)/12. More generally, the values of xi(w(1),...w(k)) and (ξ) over tilde (w(1)'...,w(k)') are determined for all k greater than or equal to 2, w(1), w(2) greater than or equal to 1, w(3),...,w(k) is an element of [0, infinity) and all w(1)',...,w(k)' is an element of [0, infinity). 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. (C) 2002 Editions scientifiques et medicales Elsevier SAS.