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作者：Dello Schiavo, Lorenzo; Portinale, Lorenzo; Sau, Federico
作者单位：Institute of Science & Technology - Austria; University of Bonn; University of Catania
摘要：We consider the open symmetric exclusion (SEP) and inclusion (SIP) processes on a bounded Lipschitz domain Omega, with both fast and slow boundary. For the random walks on Omega dual to SEP/SIP we establish: a functional-CLT-type convergence to the Brownian motion on Omega with either Neumann (slow boundary), Dirichlet (fast boundary), or Robin (at criticality) boundary conditions; the discrete-to-continuum convergence of the corresponding harmonic profiles. As a consequence, we rigorously der...
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作者：Peca-Medlin, John
作者单位：University of Arizona
摘要：Gaussian elimination with partial pivoting (GEPP) is a widely usedmethod to solve dense linear systems. Each GEPP step uses a row transposi-tion pivot movement if needed to ensure the leading pivot entry is maximalin magnitude for the leading column of the remaining untriangularized sub-system. We will use theoretical and numerical approaches to study how oftenthis pivot movement is needed. We provide full distributional descriptions forthe number of pivot movements needed using GEPP using par...
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作者：Wang, Zhichao; Zhu, Yizhe
作者单位：University of California System; University of California San Diego; University of California System; University of California Irvine
摘要：In this paper, we investigate a two -layer fully connected neural network of the form f (X) = 1/root d(1) a(T )sigma (W X ), where X is an element of (d0xn) is a deterministic data matrix, W is an element of R-d1xd0 and a is an element of R-d1 are random Gaussian weights, and sigma is a nonlinear activation function. We study the limiting spectral distributions of two empirical kernel matrices associated with f (X): the empirical conjugate kernel (CK) and neural tangent kernel (NTK), beyond th...
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作者：Izyurov, Konstantin; Kemppainen, Antti; Tuisku, Petri
作者单位：University of Helsinki
摘要：We compute rigorously the scaling limit of multipoint energy correlations in the critical Ising model on a torus. For the one -point function, averaged between horizontal and vertical edges of the square lattice, this result has been known since the 1969 work of Ferdinand and Fischer. We propose an alternative proof, in a slightly greater generality, via a new exact formula in terms of determinants of discrete Laplacians. We also compute the main term of the asymptotics of the difference E(EV ...
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作者：Bruned, Yvain; Nadeem, Usama
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; University of Edinburgh; Heriot Watt University
摘要：In this work, we show a convergence result for the discrete formulation of the generalised KPZ equation Bt u = (Au) +g(u)(Vu)2 +k(Vu) +h(u) + f (u)xi t(x), where xi is real -valued, A is the discrete Laplacian, and V is a discrete gradient, without fixing the spatial dimension. Our convergence result is established within the discrete regularity structures introduced by Hairer and Erhard (Ann. Inst. Henri Poincare Probab. Stat. 55 (2019) 2209-2248). We extend with new ideas the convergence res...
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作者：Ziliotto, Bruno
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
摘要：In a zero -sum stochastic game with signals (Repeated Games (2015) Cambridge Univ. Press, Chapter IV), at each stage, two adversary players make decisions and receive stage payoffs determined by these decisions and a variable called the state. The state follows a Markov chain controlled by both players. Actions and states are imperfectly observed by players, who receive private signals at each stage. Mertens (In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, ...
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作者：Nachmias, Asaf; Tang, Pengfei
作者单位：Tel Aviv University; Tianjin University
摘要：We study the spectral and diffusive properties of the wired minimal span-ning forest (WMSF) on the Poisson-weighted infinite tree (PWIT). LetMbethe tree containing the root in the WMSF on the PWIT and(Y-n)(n >= 0)be asimple random walk onMstarting from the root. We show that almost surelyMhasP[Y-2n=Y-0]=n-(3/4+o(1))and dist(Y-0,Y-n)=n(1/4+o(1))with highprobability. That is, the spectral dimension ofMis 3/2 and its typical dis-placement exponent is 1/4, almost surely. These confirm Addario-Berr...
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作者：Davydova, Michel
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson hypothesis regime replaces interaction times between neurons by Poisson processes. We prove that the Poisson hypothesis holds at the limit of an infinite number of replicas in the replica-mean-field model, which consists of randomly ...
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作者：Fang, Xiao; Koike, Yuta
作者单位：Chinese University of Hong Kong; University of Tokyo
摘要：We prove the large-dimensional Gaussian approximation of a sum ofnindependent random vectors inRdtogether with fourth-moment error boundson convex sets and Euclidean balls. Our bounds have near-optimal depen-dence onnand, compared with classical third-moment bounds, can achieveimproved dependence on the dimensiond. For centered balls, we obtain anadditional error bound that has a sub-optimal dependence onn, but recoversthe known result of the validity of the Gaussian approximation if and onlyi...
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作者：Cox, Alexander M. G.; Kallblad, Sigrid; Larsson, Martin; Svaluto-Ferro, Sara
作者单位：University of Bath; Royal Institute of Technology; Carnegie Mellon University; University of Verona
摘要：We consider a class of stochastic control problems where the state process is a probability measure -valued process satisfying an additional martingale condition on its dynamics, called measure -valued martingales (MVMs). We establish the classical results of stochastic control for these problems: specifically, we prove that the value function for the problem can be characterised as the unique solution to the Hamilton-Jacobi-Bellman equation in the sense of viscosity solutions. In order to pro...
