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作者：Chevyrev, Ilya; Friz, Peter K.; Korepanov, Alexey; Melbourne, Ian
作者单位：University of Edinburgh; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Exeter; University of Warwick
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作者：Han, Yanjun; Jiao, Jiantao; Mukherjee, Rajarshi
作者单位：Stanford University; University of California System; University of California Berkeley; Harvard University; Harvard T.H. Chan School of Public Health
摘要：We provide a complete picture of asymptotically minimax estimation of L-r-norms (for any r >= 1) of the mean in Gaussian white noise model over Nikolskii-Besov spaces. In this regard, we complement the work of Lepski et al. (Probab Theory Relat Fields 113(2):221-253, 1999), who considered the cases of r = 1 (with poly-logarithmic gap between upper and lower bounds) and r even (with asymptotically sharp upper and lower bounds) over Holder spaces. We additionally consider the case of asymptotica...
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作者：Eskenazis, Alexandros; Ivanisvili, Paata
作者单位：Princeton University; University of California System; University of California Irvine; Sorbonne Universite; Universite Paris Cite
摘要：Let (X, parallel to . parallel to(X)) be a Banach space. The purpose of this article is to systematically investigate dimension independent properties of vector valued functions f : {-1, 1}(n) -> X on the Hamming cube whose spectrum is bounded above or below. Our proofs exploit contractivity properties of the heat flow, induced by the geometry of the target space (X, parallel to . parallel to (X)), combined with duality arguments and suitable tools from approximation theory and complex analysi...
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作者：Zhang, Deng
作者单位：Shanghai Jiao Tong University
摘要：We study optimal control problems for stochastic nonlinear Schrodinger equations in both the mass subcritical and critical case. For general initial data of the minimal L-2 regularity, we prove the existence and first order Lagrange condition of an open loop control. In particular, these results apply to the stochastic nonlinear Schrodinger equations with the critical quintic and cubic nonlinearities in dimensions one and two, respectively. Furthermore, we obtain uniform estimates of (backward...
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作者：Lyons, Russell; White, Graham
作者单位：Indiana University System; Indiana University Bloomington
摘要：Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk, but whose duals have only a singular stationary measure. This answers a question of Curien and shows behaviour different from the unimodular case. The consequence is that planar duality does not combine well with stationary random graphs. We also study harmonic measure on dyadic lattice graph...
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作者：Peres, Yuval; Tanaka, Ryokichi; Zhai, Alex
作者单位：Tohoku University; University System of Ohio; Kent State University; Kent State University Salem; Kent State University Kent; Stanford University
摘要：We analyze a Markov chain, known as the product replacement chain, on the set of generating n-tuples of a fixed finite group G. We show that as n. 8, the totalvariation mixing time of the chain has a cutoff at time 3 2 n log n with window of order n. This generalizes a result of Ben-Hamou and Peres (who established the result for G = Z/2) and confirms a conjecture of Diaconis and Saloff-Coste that for an arbitrary but fixed finite group, the mixing time of the product replacement chain is O(n ...
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作者：Burdzy, Krzysztof; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we consider a sequence of partitions of the edges of the metric graph with the partition size going to zero. As the mesh of the subdivision goes to zero, the conditioned random labelings converge, in a suitable sense, to a deterministic function which evolves as ...
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作者：Aru, Juhan; Lupu, Titus; Sepulveda, Avelio
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We introduce the first passage set (FPS) of constant level -a of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of points in the domain that can be connected to the boundary by a path on which the GFF does not go below -a. It is, thus, the two-dimensional analogue of the first hitting time of -a by a one-dimensional Brownian motion. We provide an axiomatic characterization of the FPS, a continuum construction using level lines, ...
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作者：Gigli, Nicola; Tamanini, Luca
作者单位：International School for Advanced Studies (SISSA); University of Bonn
摘要：In this paper we prove that, within the framework of RCD* (K, N) spaces with N < infinity, the entropic cost (i.e. the minimal value of the Schrodinger problem) admits: A threefold dynamical variational representation, in the spirit of the Benamou-Brenier formula for the Wasserstein distance; A Hamilton-Jacobi-Bellman dual representation, in line with Bobkov-Gentil-Ledoux and Otto-Villani results on the duality between Hamilton-Jacobi and continuity equation for optimal transport; A Kantorovic...
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作者：Gordina, Maria; Roeckner, Michael; Teplyaev, Alexander
作者单位：University of Connecticut; University of Bielefeld; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We consider a perturbation of a Hilbert space-valued Ornstein-Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts. The only further assumption on the drift is that it is bounded on balls in the Hilbert space uniformly in time. First we introduce a new notion of generalized solutions for such equations which we call pseudo-weak solutions and prove that they always exist and obtain pathwise estimates in terms of the data of the equation. Then ...
