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作者：Bordenave, Charles; Caputo, Pietro; Salez, Justin
作者单位：Roma Tre University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Paris Cite; Universite Paris Cite
摘要：We study convergence to equilibrium for a class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix P the mass is essentially concentrated on few entries. Moreover, the entries are exchangeable within each row. This includes various models of random walks on sparse random directed graphs. The models are generally non reversible and the equilibrium distribution is itself unknown. In this general setting we establish the cutoff ph...
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作者：Boyer, Jean-Baptiste
作者单位：Universite Paris Saclay
摘要：Let be a probability measure on :=SLd(Z). Consider the random walk defined by on the torus Td=Rd/Zd: for any xTd, the walk starting at x is defined by where (gn)N is chosen with the law circle times N. Bourgain, Furmann, Lindenstrauss and Mozes proved that under an assumption on the group generated by the support of , the random walk starting at any irrational point equidistributes in the torus. In this article, we study the Functional Central Limit Theorem and the almost sure Functional Centr...
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作者：Berger, Quentin
作者单位：Sorbonne Universite
摘要：The goal of these notes is to fill some gaps in the literature about random walks in the Cauchy domain of attraction, which has often been left aside because of its additional technical difficulties. We prove here several results in that case: a Fuk-Nagaev inequality and a local version of it; a large deviation theorem; two types of local large deviation theorems. We also derive two important applications of these results: a sharp estimate of the tail of the first ladder epochs, and renewal th...
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作者：Li, Jhih-Huang
作者单位：University of Geneva
摘要：We study the interface in the FK-representation of the 1D quantum Ising model and show that in the limit, it converges to the SLE16/3 curve.
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作者：Flandoli, Franco; Luo, Dejun
作者单位：Scuola Normale Superiore di Pisa; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
摘要：A stochastic version of 2D Euler equations with transport type noise in the vorticity is considered, in the framework of Albeverio-Cruzeiro theory (Commun Math Phys 129:431-444, 1990) where the equation is considered with random initial conditions related to the so called enstrophy measure. The equation is studied by an approximation scheme based on random point vortices. Stochastic processes solving the Euler equations are constructed and their density with respect to the enstrophy measure is...
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作者：Klopp, Olga; Verzelen, Nicolas
作者单位：ESSEC Business School; Institut Polytechnique de Paris; ENSAE Paris; INRAE
摘要：Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block constant matrices and step function graphons. Surprisingly, our results imply that, from the minimax point of view, the raw data, that is, the adjacency matrix of the observed graph, is already optimal and more involved procedures cannot improve the convergen...
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作者：Dwivedi, Raaz; Feldheim, Ohad N.; Gurel-Gurevich, Ori; Ramdas, Aaditya
作者单位：University of California System; University of California Berkeley; Hebrew University of Jerusalem
摘要：Consider an infinite sequence of independent, uniformly chosen points from [0,1]d. After looking at each point in the sequence, an overseer is allowed to either keep it or reject it, and this choice may depend on the locations of all previously kept points. However, the overseer must keep at least one of every two consecutive points. We call a sequence generated in this fashion a two-thinning sequence. Here, the purpose of the overseer is to control the discrepancy of the empirical distributio...
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作者：Dolega, Maciej; Sniady, Piotr
作者单位：Adam Mickiewicz University; University of Wroclaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a deformation which is related to Jack polynomials and Jack characters. We show that each such a random Young diagram converges asymptotically to some limit shape and that the fluctuations around the limit are asymptotically Gaussian.
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作者：Duminil-Copin, Hugo; Raoufi, Aran; Tassion, Vincent
作者单位：University of Geneva; Universite Paris Saclay; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that for Voronoi percolation on Rd(d2), there exists pc=pc(d)(0,1) such thatfor p0 such that Pp[0connected to distancen]exp(-cpn),there exists c>0 such that for p>pc,Pp[0connected to infinity]c(p-pc). For dimension 2, this result offers a new way of showing that pc(2)=1/2. This paper belongs to a series of papers using the theory of algorithms to prove sharpness of the phase transition; see [10, 11].
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作者：Fan, Zhou; Montanari, Andrea
作者单位：Stanford University; Stanford University
摘要：We study an inner-product kernel random matrix model, whose empirical spectral distribution was shown by Xiuyuan Cheng and Amit Singer to converge to a deterministic measure in the large n and p limit. We provide an interpretation of this limit measure as the additive free convolution of a semicircle law and a Marchenko-Pastur law. By comparing the tracial moments of this matrix to an additive deformation of a Wigner matrix, we establish that for odd kernel functions, the spectral norm of this...
