Finite-Size Left-Passage Probability in Percolation

Article Article scientifique Article Finite-Size Left-Passage Probability in Percolation eng 2012 author Ikhlef Yacine 707485 author Ponsaing Anita Kristine 763281 10-36 10.1007/s10955-012-0573-z 0022-4715 We obtain an exact finite-size expression for the probability that a percolation hull will touch the boundary, on a strip of finite width. In terms of clusters, this corresponds to the one-arm probability. Our calculation is based on the q-deformed Knizhnik–Zamolodchikov approach, and the results are expressed in terms of symplectic characters. In the large size limit, we recover the scaling behaviour predicted by Schramm's left-passage formula. We also derive a general relation between the left-passage probability in the Fortuin–Kasteleyn cluster model and the magnetisation profile in the open XXZ chain with diagonal, complex boundary terms. Dewey 510 Open Access - Licence nationale Springer 25 Section de mathématiques 11 false Journal of Statistical Physics 149 1 db25ef39-9604-4253-909e-5159f5e039d3 Article (Published version) Public Ikhlef-Ponsaing2012_Article_Finite-SizeLeft-PassageProbabi.pdf 1055955 application/pdf openAccess Faculté des sciences / Section de mathématiques

Title	Published in	Access level	OA Policy	Year	Views	Downloads

Finite-Size Left-Passage Probability in Percolation	Journal of Statistical Physics			2012	343	328

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Ponsaing, Anita Kristine