作者：Camia, Federico; Newman, Charles M.
作者单位：Vrije Universiteit Amsterdam; New York University
摘要：It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE6. We provide here a detailed proof, which relies on Smirnov's theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy's formula). The version of convergence to SLE (6) that we prove suffices for the Smirnov-Werner derivation of certain critical percolation crossing exponents and for our an...
作者：Schapira, Bruno
作者单位：Universite de Orleans; Universite Paris Cite; Sorbonne Universite
摘要：We introduce and study the natural counterpart of the Dunkl Markov processes in a negatively curved setting. We give a semimartingale decomposition of the radial part, and some properties of the jumps. We prove also a law of large numbers, a central limit theorem, and the convergence of the normalized process to the Dunkl process. Eventually we describe the asymptotic behavior of the infinite loop as it was done by Anker, Bougerol and Jeulin in the symmetric spaces setting in (Iberoamericana 1...
