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作者：Chinot, Geoffrey; Lecue, Guillaume; Lerasle, Matthieu
摘要：We obtain estimation and excess risk bounds for Empirical Risk Minimizers (ERM) and minmax Median-Of-Means (MOM) estimators based on loss functions that are both Lipschitz and convex. Results for the ERM are derived under weak assumptions on the outputs and subgaussian assumptions on the design as in Alquier et al. (Estimation bounds and sharp oracle inequalities of regularized procedures with Lipschitz loss functions. arXiv:1702.01402, 2017). The difference with Alquier et al. (2017) is that ...
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作者：Damron, Michael; Sen, Arnab
作者单位：University System of Georgia; Georgia Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities
摘要：In zero-temperature Glauber dynamics, vertices of a graph are given i.i.d. initial spins sigma(x) (0) from {-1,+1} with P-p(sigma(x) (0) = +1) = p, and they update their spins at the arrival times of i.i.d. Poisson processes to agree with a majority of their neighbors. We study this process on the 3-regular tree T-3, where it is known that the critical threshold p(c), below which Pp-a.s. all spins fixate to -1, is strictly less than 1/2. Defining theta(p) to be the P-p-probability that a verte...
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作者：Ding, Jian; Fukushima, Ryoki; Sun, Rongfeng; Xu, Changji
作者单位：University of Pennsylvania; Kyoto University; National University of Singapore; University of Chicago
摘要：We consider a discrete time simple symmetric random walk among Bernoulli obstacles on Z(d), d >= 2, where the walk is killed when it hits an obstacle. It is known that conditioned on survival up to time N, the random walk range is asymptotically contained in a ball of radius (sic)N = CN1/(d+ 2) for any d = 2. For d = 2, it is also known that the range asymptotically contains a ball of radius (1-) N for any > 0, while the case d = 3 remains open. We complete the picture by showing that for any ...
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作者：Osada, Hirofumi; Tanemura, Hideki
作者单位：Kyushu University; Keio University
摘要：We present general theorems solving the long-standing problem of the existence and pathwise uniqueness of strong solutions of infinite-dimensional stochastic differential equations (ISDEs) called interacting Brownian motions. These ISDEs describe the dynamics of infinitely-many Brownian particles moving in R-d with free potential Phi and mutual interaction potential Psi. We apply the theorems to essentially all interaction potentials of Ruelle's class such as the Lennard-Jones 6-12 potential a...
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作者：Beiglboeck, Mathias; Cox, Alexander M. G.; Huesmann, Martin
作者单位：University of Vienna; University of Bath
摘要：The Skorokhod Embedding Problem is one of the classical problems in the theory of stochastic processes, with applications in many different fields [cf. the surveys (Hobson in: Paris-Princeton lectures on mathematical finance 2010, Volume 2003 of Lecture Notes in Mathematics, Springer, Berlin, 2011; Oboj in: Probab Surv 1:321-390, 2004)]. Many of these applications have natural multi-marginal extensions leading to the (optimal) multi-marginal Skorokhod problem. Some of the first papers to consi...
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作者：Peres, Yuval; Sousi, Perla; Steif, Jeffrey E.
作者单位：Microsoft; University of Cambridge; Chalmers University of Technology; University of Gothenburg
摘要：We consider dynamical percolation on the d-dimensional discrete torus Zndof side length n, where each edge refreshes its status at rate mu=mu n <= 1/2 to be open with probability p. We study random walk on the torus, where the walker moves at rate 1 / (2d) along each open edge. In earlier work of two of the authors with A. Stauffer, it was shown that in the subcritical case p1/2. When theta(p)>0, we prove a version of this conjecture for an alternative notion of mixing time involving randomise...
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作者：Pal, Soumik; Wong, Ting-Kam Leonard
作者单位：University of Washington; University of Washington Seattle; University of Toronto
摘要：We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show that the optimal transport is the large deviation limit of a particle system of Dirichlet processes transporting one probability measure on the unit simplex to another by coordinatewise multiplication and normalizing. The structure of our Lagrangian and the appearance of the Dirichlet process relate our problem closely...
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作者：Duerinckx, Mitia; Gloria, Antoine; Otto, Felix
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Universite Libre de Bruxelles; Max Planck Society
摘要：We consider a linear elliptic system in divergence form with random coefficients and study the random fluctuations of large-scale averages of the field and the flux of the solution operator. In the context of the random conductance model, we developed in a previous work a theory of fluctuations based on the notion of homogenization commutator: we proved that the two-scale expansion of this special quantity is accurate at leading order in the fluctuation scaling when averaged on large scales (a...
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作者：Belius, David; Rosen, Jay; Zeitouni, Ofer
作者单位：University of Basel; City University of New York (CUNY) System; College of Staten Island (CUNY); Weizmann Institute of Science; New York University
摘要：Let CE,S2 denote the cover time of the two dimensional sphere by a Wiener sausage of radius E. We prove that CE,S2AS2 pi logE-1-loglogE-1is tight, where AS2=4 pi denotes the Riemannian area of S2.
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作者：Dumaz, Laure; Labbe, Cyril
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
摘要：We study the bottom of the spectrum of the Anderson Hamiltonian H-L := -partial derivative(2)(x) + xi on [0, L] driven by a white noise xi and endowed with either Dirichlet or Neumann boundary conditions. We show that, as L -> infinity, the point process of the (appropriately shifted and rescaled) eigenvalues converges to a Poisson point process on R with intensity e(x)dx, and that the (appropriately rescaled) eigenfunctions converge to Dirac masses located at independent and uniformly distrib...
