Values of Brownian intersection exponents III: Two-sided exponents
Lawler, Gregory F. ; Schramm, Oded ; Werner, Wendelin
arXiv, 0005294 / Harvested from arXiv
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.
Publié le : 2000-05-31
Classification:  Mathematics - Probability,  Mathematical Physics,  Mathematics - Complex Variables,  60J65,  30C35,  82B41,  82B43
@article{0005294,
     author = {Lawler, Gregory F. and Schramm, Oded and Werner, Wendelin},
     title = {Values of Brownian intersection exponents III: Two-sided exponents},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0005294}
}
Lawler, Gregory F.; Schramm, Oded; Werner, Wendelin. Values of Brownian intersection exponents III: Two-sided exponents. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0005294/