Excursion decompositions for SLE and Watts' crossing formula

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Abstract

It is known that Schramm-Loewner Evolutions (SLEs) have a.s. frontier points if κ>4 and a.s. cutpoints if 4 4, an appropriate version of SLE(κ) has a renewal property: it starts afresh after visiting its frontier. Thus one can give an excursion decomposition for this particular SLE(κ) "away from its frontier". For 4

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Dubédat, J. (2006). Excursion decompositions for SLE and Watts’ crossing formula. Probability Theory and Related Fields, 134(3), 453–488. https://doi.org/10.1007/s00440-005-0446-3

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