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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：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...
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作者：Chapuy, Guillaume
作者单位：Universite Paris Cite
摘要：We study the masses of the two cells in a Voronoi tessellation of the Brownian surface of genus g0 centered on two uniform random points. Making use of classical bijections and asymptotic estimates for maps of fixed genus, we relate the second moment of these random variables to the Painleve-I equation satisfied by the double scaling limit of the one-matrix model, or equivalently to the tg-recurrence satisfied by the constants tg driving the asymptotic number of maps of genus g0. This raises t...
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作者：Zhan, Dapeng
作者单位：Michigan State University
摘要：We make use of the fact that a two-sided whole-plane Schramm-Loewner evolution (SLE kappa) curve gamma for kappa is an element of (0, 8) from infinity to infinity through 0 may be parametrized by its d-dimensional Minkowski content, where d = 1 + kappa/8, and become a self-similar process of index 1/d with stationary increments. We prove that such gamma is locally alpha-Holder continuous for any alpha < 1/d. In the case kappa is an element of (0, 4], we show that gamma is not locally 1/d-Holde...
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作者：Cerrai, Sandra; Freidlin, Mark
作者单位：University System of Maryland; University of Maryland College Park
摘要：Fast advection asymptotics for a stochastic reaction-diffusion-advection equation are studied in this paper. To describe the asymptotics, we introduce a new class of SPDEs defined on a graph, corresponding to the stream function of the underlying incompressible flow. We prove that, as the advection term becomes faster and faster, the solution of the stochastic reaction-diffusion-advection equation on the plane converges in a suitable sense to the solution of such an SPDE defined on the graph. ...
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作者：Gorin, Vadim; Rahman, Mustazee
作者单位：Massachusetts Institute of Technology (MIT); Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：This paper finds the bulk local limit of the swap process of uniformly random sorting networks. The limit object is defined through a deterministic procedure, a local version of the Edelman-Greene algorithm, applied to a two dimensional determinantal point process with explicit kernel. The latter describes the asymptotic joint law near 0 of the eigenvalues of the corners in the antisymmetric Gaussian Unitary Ensemble. In particular, the limiting law of the first time a given swap appears in a ...
