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作者：Mentemeier, Sebastian
作者单位：University of Wroclaw
摘要：Let (T-1, T-2, . . .) be a sequence of random d x d matrices with nonnegative entries, and let Q be a random vector with nonnegative entries. Consider random vectors X with nonnegative entries, satisfying X =(L) Sigma(i >= 1) TiXi + Q, (*) where =(L) denotes equality of the corresponding laws, (X-i)(i >= 1) are i.i.d. copies of X and independent of (Q, T-1, T-2,...). For d = 1, this equation, known as fixed point equation of the smoothing transform, has been intensively studied. Under assumpti...
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作者：Capitaine, Mireille; Peche, Sandrine
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We consider a full rank deformation of the GUE where is a full rank Hermitian matrix of size and is a GUE. The empirical eigenvalue distribution of converges to a probability distribution . We identify all the possible limiting eigenvalue statistics at the edges of the spectrum, including outliers, edges and merging points of connected components of the limiting spectrum. The results are stated in terms of a deterministic equivalent of the empirical eigenvalue distribution of , namely the free...
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作者：Herdade, Simo; Vu, Van
作者单位：Rutgers University System; Rutgers University New Brunswick; Yale University
摘要：As an extension of Polya's classical result on random walks on the square grids (), we consider a random walk where the steps, while still have unit length, point to different directions. We show that in dimensions at least 4, the returning probability after n steps is at most , which is sharp. The real surprise is in dimensions 2 and 3. In dimension 2, where the traditional grid walk is recurrent, our upper bound is , which is much worse than in higher dimensions. In dimension 3, we prove an ...
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作者：De Santis, Emilio; Maffei, Andrea
作者单位：Sapienza University Rome; University of Pisa
摘要：In this article we create a new algorithm for the perfect simulation of the infinite random cluster model for a sufficiently small or a sufficiently high value of the parameters. This implies the simulation of the Ising and Potts models with free boundary conditions.
