Universality for conformally invariant intersection exponents

Lawler, Gregory, and Werner, Wendelin. "Universality for conformally invariant intersection exponents." Journal of the European Mathematical Society 002.4 (2000): 291-328. <http://eudml.org/doc/277269>.

@article{Lawler2000,
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.},
author = {Lawler, Gregory, Werner, Wendelin},
journal = {Journal of the European Mathematical Society},
keywords = {conformally invariant measure; intersection exponent; planar Brownian motion},
language = {eng},
number = {4},
pages = {291-328},
publisher = {European Mathematical Society Publishing House},
title = {Universality for conformally invariant intersection exponents},
url = {http://eudml.org/doc/277269},
volume = {002},
year = {2000},
}

TY - JOUR
AU - Lawler, Gregory
AU - Werner, Wendelin
TI - Universality for conformally invariant intersection exponents
JO - Journal of the European Mathematical Society
PY - 2000
PB - European Mathematical Society Publishing House
VL - 002
IS - 4
SP - 291
EP - 328
AB - 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.
LA - eng
KW - conformally invariant measure; intersection exponent; planar Brownian motion
UR - http://eudml.org/doc/277269
ER -