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作者：Chen, Yue; Busic, Ana; Meyn, Sean
作者单位：State University System of Florida; University of Florida; Inria; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Consider a stochastic process X on a finite state space X = {1,...,}d. It is conditionally Markov, given a real-valued input process sigma.0 This is assumed to be small, which is modeled through the scaling, sigma(t) = epsilon sigma(1)(t), 0 <= epsilon <= 1, where sigma(1) is a bounded stationary process. The following conclusions are obtained, subject to smoothness assumptions on the controlled transition matrix and a mixing condition on sigma : (i) A stationary version of the process is cons...
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作者：Pichler, Georg; Piantanida, Pablo; Matz, Gerald
作者单位：Technische Universitat Wien; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：Let (X, Y) denote n independent, identically distributed copies of two arbitrarily correlated Rademacher random variables (X, Y). We prove that the inequality I( f (X); g (Y)) <= I(X; Y) holds for any two Boolean functions: f, g: {-1,1}(n) -> {-1,1} [I(.;.) denotes mutual information]. We further show that equality in general is achieved only by the dictator functions f(x) = +/- g(x) = +/- x(i), i is an element of {1,2,...,n}.
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作者：Deaconu, Madalina; Herrmann, Samuel
作者单位：Inria; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Bourgogne Europe; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The initial-boundary value problem for the heat equation is solved by using an algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to solve the Dirichlet problem for Laplace's equation, its implementation is rather easy. The construction of this algorithm can be considered as a natural consequence of previous works the authors completed on the hitting time approximation for Bessel processes and B...
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作者：Briand, Philippe; Elie, Romuald; Hu, Ying
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Savoie Mont Blanc; CNRS - National Institute for Mathematical Sciences (INSMI); CNRS - Institute of Physics (INP); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite Gustave-Eiffel; Inria; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we study a new type of BSDE, where the distribution of the Y-component of the solution is required to satisfy an additional constraint, written in terms of the expectation of a loss function. This constraint is imposed at any deterministic time t and is typically weaker than the classical pointwise one associated to reflected BSDEs. Focusing on solutions (Y, Z, K) with deterministic K, we obtain the well-posedness of such equation, in the presence of a natural Skorokhod-type con...
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作者：Ye, Heng-Qing; Yao, David D.
作者单位：Hong Kong Polytechnic University; Columbia University
摘要：Multiclass queueing networks (MQN) are, in general, difficult objects to study analytically. The diffusion approximation refers to using the stationary distribution of the diffusion limit as an approximation of the diffusion-scaled process (say, the workload) in the original MQN. To validate such an approximation amounts to justifying the interchange of two limits, t -> infinity and k -> infinity, with t being the time index and k, the scaling parameter. Here, we show this interchange of limit...
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作者：Bella, Peter; Fehrman, Benjamin; Otto, Felix
作者单位：Leipzig University; Max Planck Society
摘要：We study the behavior of second-order degenerate elliptic systems in divergence form with random coefficients which are stationary and ergodic. Assuming moment bounds like Chiarini and Deuschel (2014) on the coefficient field a and its inverse, we prove an intrinsic large-scale C-1,C-alpha-regularity estimate for a-harmonic functions and obtain a first-order Liouville theorem for a-harmonic functions.
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作者：Chen, Wei-Kuo; Panchenk, Dmitry
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Toronto
摘要：We prove disorder chaos at zero temperature for three types of diluted models with large connectivity parameter: K-spin antiferromagnetic Ising model for even K >= 2, K-spin spin glass model for even K >= 2, and random K-sat model for all K >= 2. We show that modifying even a small proportion of clauses results in near maximizers of the original and modified Hamiltonians being nearly orthogonal to each other with high probability. We use a standard technique of approximating diluted models by ...
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作者：Chen, Yu-Ting
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We investigate stochastic spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the one-dimensional Wright-Fisher diffusions. Convergence in the Wasserstein distance of the laws of the occupation measures also holds. The proofs study the convergences under certain voter models by an equivalence between their laws and the laws of the ev...
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作者：Bhamidi, Shankar; Jin, Jimmy; Nobel, Andrew
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Inspired by empirical data on real world complex networks, the last few years have seen an explosion in proposed generative models to understand and explain observed properties of real world networks, including power law degree distribution and small world distance scaling. In this context, a natural question is how to understand the effect of change points-how abrupt changes in parameters driving the network model change structural properties of the network. We study this phenomenon in one po...
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作者：Gnedin, Alexander; Iksanov, Alexander; Marynych, Alexander; Moehle, Martin
作者单位：University of London; Queen Mary University London; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; Eberhard Karls University of Tubingen
摘要：Lambda-coalescents model the evolution of a coalescing system in which any number of blocks randomly sampled from the whole may merge into a larger block. For the coalescent restricted to initially n singletons, we study the collision spectrum (X-n,X- k : 2 <= k <= n), where X-n,X- k counts, throughout the history of the process, the number of collisions involving exactly k blocks. Our focus is on the large n asymptotics of the joint distribution of the X-n,X- k's, as well as on functional lim...
