2000/05/31 by Gregory F. Lawler, Oded Schramm, Wendelin Werner · 4 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Brownian bridge #Brownian motion #Combinatorics #Exponent #Geometry #Intersection (aeronautics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Planar #Plane (geometry) #Probability and Risk Models #Quantum mechanics #Statistics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Universality (dynamical systems) #math-ph #math.CV #math.MP #math.PR #msc:30C35 #msc:60J65 #msc:82B41 #msc:82B43
paper · pdf · doi:10.1016/s0246-0203(01)01089-5
published as Ann.Inst.H.PoincareProbab.Statist.38:109-123,2002
arxiv created 2000/05/31 · openalex publication_date 2002/01/01 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \tx (w1', ..., wk') are determined for all k ≥ 2, w1, w2≥ 1, w3, ...,wk∈[0,∞) and all w1',...,wk'∈[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.