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作者：Marciniak, Mikolaj; Maslanka, Lukasz; Sniady, Piotr
作者单位：Nicolaus Copernicus University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We consider the Robinson-Schensted-Knuth algorithm applied to a random input and investigate the shape of the bumping route (in the vicinity of the y-axis) when a specified number is inserted into a large Plancherel-distributed random tableau. We show that after a projective change of the coordinate system the bumping route converges in distribution to the Poisson process.
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作者：Dussaule, Matthieu; Gekhtman, Ilya
作者单位：Nantes Universite; Technion Israel Institute of Technology
摘要：Let Gamma be a relatively hyperbolic group and let mu be an admissible symmetric finitely supported probability measure on Gamma. We extend Floyd-Ancona type inequalities from Gekhtman et al. (Martin boundary covers Floyd boundary, 2017. arXiv:1708.02133) up to the spectral radius R of mu. We use them to find the precise homeomorphism type of the r-Martin boundary, which describes r-harmonic functions, for every r <= R. We also define a notion of spectral degeneracy along parabolic subgroups w...
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作者：Qian, Wei
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Universite Paris Saclay
摘要：We introduce and compute the generalized disconnection exponents eta(kappa)(beta) which depend on kappa is an element of (0, 4] and another real parameter beta, extending the Brownian disconnection exponents (corresponding to kappa = 8/3) computed by Lawler, Schramm and Werner (Acta Math 187(2):275-308, 2001; Acta Math 189(2):179-201, 2002) [conjectured by Duplantier and Kwon (Phys Rev Lett 61:2514-2517, 1988)]. For kappa is an element of (8/3, 4], the generalized disconnection exponents have ...
