-
作者：Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik
作者单位：Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.
-
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...
-
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 ...
