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作者：Liu, Xuan; Qian, Zhongmin
作者单位：University of Oxford
摘要：By using analytic tools from stochastic analysis, we initiate a study of some non-linear parabolic equations on Sierpinski gasket, motivated by modellings of fluid flows along fractals (which can be considered as models of simplified rough porous media). Unlike the regular space case, such parabolic type equations involving non-linear convection terms must take a different form, due to the fact that convection terms must be singular to the linear part which defines the heat semigroup. In order...
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作者：Freslon, Amaury
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We give bounds in total variation distance for random walks associated to pure central states on free orthogonal quantum groups. As a consequence, we prove that the analogue of the uniform plane Kac walk on this quantum group has a cut-off at Nln(N)/2(1-cos(theta)). This is the first result of this type for genuine compact quantum groups. We also obtain similar results for mixtures of rotations and quantum permutations.
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作者：Levine, Lionel; Silvestri, Vittoria
作者单位：Cornell University; University of Cambridge
摘要：Internal DLA is a discrete model of a moving interface. On the cylinder graph ZNxZ, a particle starts uniformly on ZNx{0} and performs simple random walk on the cylinder until reaching an unoccupied site in ZNxZ >= 0, which it occupies forever. This operation defines a Markov chain on subsets of the cylinder. We first show that a typical subset is rectangular with at most logarithmic fluctuations. We use this to prove that two Internal DLA chains started from different typical subsets can be c...
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作者：Litvak, Alexander E.; Lytova, Anna; Tikhomirov, Konstantin; Tomczak-Jaegermann, Nicole; Youssef, Pierre
作者单位：University of Alberta; University of Opole; Princeton University; Universite Paris Cite
摘要：We derive a lower bound on the smallest singular value of a random d-regular matrix, that is, the adjacency matrix of a random d-regular directed graph. Specifically, let C1
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作者：Merkl, Franz; Rolles, Silke W. W.; Tarres, Pierre
作者单位：University of Munich; Technical University of Munich; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：In this paper, we define an extension of the supersymmetric hyperbolic nonlinear sigma model introduced by Zirnbauer. We show that it arises as a weak joint limit of a time-changed version introduced by Sabot and Tarres of the vertex-reinforced jump process. It describes the asymptotics of rescaled crossing numbers, rescaled fluctuations of local times, asymptotic local times on a logarithmic scale, endpoints of paths, and last exit trees.
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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：Duminil-Copin, Hugo; Lis, Marcin
作者单位：University of Geneva; University of Vienna
摘要：We relate the planar random current representation introduced by Griffiths, Hurst and Sherman to the dimer model. More precisely, we provide a measure-preserving map between double random currents (obtained as the sum of two independent random currents) on a planar graph and dimers on an associated bipartite graph. We also define a nesting field for the double random current, which, under this map, corresponds to the height function of the dimer model. As applications, we provide an alternativ...
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作者：Gerencser, Mate; Hairer, Martin
作者单位：Institute of Science & Technology - Austria; University of Warwick
摘要：We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269-504, 2014. 10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is...
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作者：Yao, Chang-Long
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We study Bernoulli first-passage percolation (FPP) on the triangular lattice in which sites have 0 and 1 passage times with probability p and 1- p, respectively. Denote by C8 the infinite cluster with 0-time sites when p > pc, where pc = 1/2 is the critical probability. Denote by T (0, C8) the passage time from the origin 0 to C8. First we obtain explicit limit theorem for T (0, C8) as p pc. The proof relies on the limit theorem in the critical case, the critical exponent for correlation lengt...
