Conformal Invariance and Intersections of Random Walks

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Abstract
We consider in two dimensions L (L≥2) independent Brownian paths of common lengths S, all starting at the origin, and the probability PL that their trajectories do not intersect. For S large, PL∼S−ζL where ζL is universal. In 2D the ζL's are identified as Kac conformal dimensions with c=0 central charge ζL=h0,L=(4L2−1)24, L≥2. This is generalized to L walks in a half-plane, with a common origin on the boundary.