SLE Boundary Visits

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

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We study the probabilities with which chordal Schramm-Loewner evolutions (SLE) visit small neighborhoods of boundary points. We find formulas for general chordal SLE boundary visiting probability amplitudes, also known as SLE boundary zig-zags or order refined SLE multi-point Green's functions on the boundary. Remarkably, an exact answer can be found to this important SLE question for an arbitrarily large number of marked points. The main technique employed is a spin chain-Coulomb gas correspondence between tensor product representations of a quantum group and functions given by Dotsenko-Fateev type integrals. We show how to express these integral formulas in terms of regularized real integrals, and we discuss their numerical evaluation. The results are universal in the sense that apart from an overall multiplicative constant the same formula gives the amplitude for many different formulations of the SLE boundary visit problem. The formula also applies to renormalized boundary visit probabilities for interfaces in critical lattice models of statistical mechanics: we compare the results with numerical simulations of percolation, loop-erased random walk, and Fortuin-Kasteleyn random cluster models at Q = 2 and Q = 3, and find good agreement.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut1263-1330
Sivumäärä68
JulkaisuANNALES HENRI POINCARÉ
Vuosikerta17
Numero6
TilaJulkaistu - kesäkuuta 2016
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 1982711