Universality for conformally invariant intersection exponents

Universality for conformally invariant intersection exponents We construct a class of conformally invariant measures on sets (or paths) and we study the critical exponents called intersection exponents associated to these measures. We show that these exponents exist and that they correspond to intersection exponents between planar Brownian motions. More precisely, using the definitions and results of our paper [27], we show that any set defined under such a conformal invariant measure behaves exactly as a pack (containing maybe a non-integer number) of Brownian motions as far as all intersection exponents are concerned. We show how conjectures about exponents for two-dimensional self-avoiding walks and critical percolation clusters can be reinterpreted in terms of conjectures on Brownian exponents. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

Universality for conformally invariant intersection exponents

, Volume 2 (4) – Nov 1, 2000
38 pages

/lp/springer-journals/universality-for-conformally-invariant-intersection-exponents-X5Cmi0RtSj
Publisher
Springer Journals
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970000024
Publisher site
See Article on Publisher Site

Abstract

We construct a class of conformally invariant measures on sets (or paths) and we study the critical exponents called intersection exponents associated to these measures. We show that these exponents exist and that they correspond to intersection exponents between planar Brownian motions. More precisely, using the definitions and results of our paper [27], we show that any set defined under such a conformal invariant measure behaves exactly as a pack (containing maybe a non-integer number) of Brownian motions as far as all intersection exponents are concerned. We show how conjectures about exponents for two-dimensional self-avoiding walks and critical percolation clusters can be reinterpreted in terms of conjectures on Brownian exponents.

Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Nov 1, 2000