Values of Brownian intersection exponents III: Two-sided exponents

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 (73−2 73 )/12 . More generally, the values of ξ(w1,…,wk) and ξ (w 1 ′,…,w k ′) are determined for all k⩾2, w1,w2⩾1, w3,…,wk∈[0,∞) and all w′1,…,w′k∈[0,∞). 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.