# Universality for conformally invariant intersection exponents

Gregory Lawler; Wendelin Werner

Journal of the European Mathematical Society (2000)

- Volume: 002, Issue: 4, page 291-328
- ISSN: 1435-9855

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topLawler, 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 -

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