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作者：Kroshnin, Alexey; Spokoiny, Vladimir; Suvorikova, Alexandra
作者单位：Russian Academy of Sciences; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In this work we introduce the concept of Bures-Wasserstein barycenter Q(*), that is essentially a Frechet mean of some distribution P supported on a subspace of positive semi-definite d-dimensional Hermitian operators H+(d). We allow a barycenter to be constrained to some affine subspace of H+(d), and we provide conditions ensuring its existence and uniqueness. We also investigate convergence and concentration properties of an empirical counterpart of Q(*) in both Frobenius norm and Bures-Wass...
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作者：Rockner, Michael; Yang, Huanyu; Zhu, Rongchan
作者单位：University of Bielefeld; Free University of Berlin; Beijing Institute of Technology
摘要：We consider the stochastic two-dimensional Cahn-Hilliard equation which is driven by the derivative in space of a space-time white noise. We use two different approaches to study this equation. First we prove that there exists a unique solution Y to the shifted equation (1.4). Then X := Y + Z is the unique solution to the stochastic Cahn-Hilliard equation, where Z is the corresponding O-U process. Moreover, we use the Dirichlet form approach in (Probab. Theory Related Fields 89 (1991) 347-386)...
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作者：Lagarias, Jeffrey C.; Rodgers, Brad
作者单位：University of Michigan System; University of Michigan; Queens University - Canada
摘要：We say that one point process on the line R mimics another at a band-width B if for each n >= 1 the two point processes have n-level correlation functions that agree when integrated against all band-limited test functions on bandwidth [-B, B]. This paper asks the question of for what values a and B can a given point process on the real line be mimicked at bandwidth B by a point process supported on the lattice aZ. For Poisson point processes we give a complete answer for allowed parameter rang...
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作者：de Menibus, Benjamin Hellouin; Le Borgne, Yvan
作者单位：Universite Paris Saclay; Universite de Bordeaux
摘要：The one-dimensional three-state cyclic cellular automaton is a simple spatial model with three states in a cyclic rock-paper-scissors preypredator relationship. Starting from a random configuration, similar states gather in increasingly large clusters; asymptotically, any finite region is filled with a uniform state that is, after some time, driven out by its predator, each state taking its turn in dominating the region (heteroclinic cycles). We consider the situation where each site in the in...
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作者：Kardaras, Constantinos; Robertson, Scott
作者单位：University of London; London School Economics & Political Science; Boston University
摘要：We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region E and instantaneous covariation c are known, and where the assets are stable with an exogenously given limiting density p, in that their occupancy time measures converge to a law governed by p. This latter assumption is motivated by the observed stability of ranked relative market capitalizations for equity markets....
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作者：Lil, Jia; Zhang, Congshan; Liu, Yunxiao
作者单位：Duke University; University of North Carolina; University of North Carolina Chapel Hill
摘要：We prove a Glivenko-Cantelli theorem for integrated functionals of latent continuous-time stochastic processes. Based on a bracketing condition via random brackets, the theorem establishes the uniform convergence of a sequence of empirical occupation measures towards the occupation measure induced by underlying processes over large classes of test functions, including indicator functions, bounded monotone functions, Lipschitz-in-parameter functions, and Holder classes as special cases. The gen...
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作者：Erhard, Dirk; Franco, Tertuliano; da Silva, Diogo S.
作者单位：Universidade Federal da Bahia
摘要：We consider the continuous time symmetric random walk with a slow bond on Z, which rates are equal to 1/2 for all bonds, except for the bond of vertices {-1, 0}, which associated rate is given by alpha n(-beta)/2, where alpha > 0 and beta is an element of [0, infinity] are the parameters of the model. We prove here a functional central limit theorem for the random walk with a slow bond: if beta is an element of [0, infinity), then it converges to the usual Brownian motion. If beta is an elemen...
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作者：Gamarnik, David; Kizildag, Eren C.
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In particular, we establish that unless P = #P, there does not exist a polynomial-time algorithm to exactly compute the partition function on average. This is done by showing that if there exists a polynomial time algorithm, which exactly computes the partition functi...
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作者：Calka, Pierre; Yukich, J. E.
作者单位：Universite de Rouen Normandie; Lehigh University
摘要：We consider the convex hull of the perturbed point process comprised of n i.i.d. points, each distributed as the sum of a uniform point on the unit sphere Sd-1 and a uniform point in the d-dimensional ball centered at the origin and of radius n(alpha), alpha is an element of (-infinity,infinity). This model, inspired by the smoothed complexity analysis introduced in computational geometry (J. Comput. Geom. 7 (2016) 101-144; J. ACM 51 (2004) 385-463), is a perturbation of the classical random p...
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作者：Schapira, Bruno
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We continue the investigation of the localization phenomenon for a vertex reinforced random walk on the integer lattice. We provide some partial results towards a full characterization of the weights for which localization on 5 sites occurs with positive probability, and make some conjecture concerning the almost sure behavior.
