Mathematics – Probability
Scientific paper
2000-05-31
Ann.Inst.H.PoincareProbab.Statist.38:109-123,2002
Mathematics
Probability
Scientific paper
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 $(73-2 \sqrt {73}) / 12$. More generally, the values of $\xi (w_1, >..., w_k)$ and $\tx (w_1', ..., w_k')$ are determined for all $ k \ge 2$, $w_1, w_2\ge 1$, $w_3, ...,w_k\in[0,\infty)$ 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.
Lawler Gregory F.
Schramm Oded
Werner Wendelin
No associations
LandOfFree
Values of Brownian intersection exponents III: Two-sided exponents does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Values of Brownian intersection exponents III: Two-sided exponents, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Values of Brownian intersection exponents III: Two-sided exponents will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-362445