On Crossing Event Formulas in Critical Two-Dimensional Percolation

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dc.creatorMaier, Robert S.
dc.date2002-10-07
dc.date2002-12-10
dc.date.accessioned2026-07-07T04:29:28Z
dc.date.available2026-07-07T04:29:28Z
dc.descriptionSeveral formulas for crossing functions arising in the continuum limit of critical two-dimensional percolation models are studied. These include Watts's formula for the horizontal-vertical crossing probability and Cardy's new formula for the expected number of crossing clusters. It is shown that under the assumption of conformal invariance, they simplify when the spatial domain is taken to be the interior of an equilateral triangle. The two crossing functions can be expressed in terms of an equianharmonic elliptic function with a triangular rotational symmetry. This suggests that rigorous proofs of Watts's formula and Cardy's new formula will be easiest to construct if the underlying lattice is triangular. The simplification in a triangular domain of Schramm's `bulk Cardy's formula' is also studied.
dc.descriptionfinal version, accepted by J. Statistical Physics; 22 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0210013
dc.identifierhttp://arxiv.org/abs/math-ph/0210013
dc.identifierJ. Statistical Physics 111 (2003) 1027-1048
dc.identifierdoi:10.1023/A:1023006413433
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57170
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.titleOn Crossing Event Formulas in Critical Two-Dimensional Percolation
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