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作者：Ivanovs, Jevgenijs
作者单位：Aarhus University
摘要：Let M and iota be the supremum and its time of a Levy process X on some finite time interval. It is shown that zooming in on X at its supremum, that is, considering ((X tau+t epsilon - M)/a epsilon)(t is an element of R) as e down arrow 0, results in (xi(t))(t is an element of R) constructed from two independent processes having the laws of some self-similar Levy process (X) over cap conditioned to stay positive and negative. This holds when X is in the domain of attraction of (X) over cap und...
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作者：Lipshutz, David; Ramanan, Kavita
作者单位：Brown University
摘要：The study of both sensitivity analysis and differentiability of the stochastic flow of a reflected process in a convex polyhedral domain is challenging due to the abrupt change in the nature of the dynamics at the boundary and is further complicated because the boundary is not smooth. These difficulties can be addressed by studying directional derivatives of an associated extended Skorokhod map, which is a deterministic mapping that takes an unconstrained path to a suitably reflected or constr...
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作者：Aghajani, Reza; Robert, Philippe; Sun, Wen
作者单位：University of California System; University of California San Diego
摘要：The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all copies of files stored on it are lost. In this way, repeated failures may lead to losses of files. The efficiency of such a network is directly related to the performances of the mechanism used to duplicate files on servers. In this paper, we study the evolution ...
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作者：Berestycki, Nathanael; Zhao, Lee Zhuo
作者单位：University of Cambridge
摘要：We introduce particle systems in one or more dimensions in which particles perform branching Brownian motion and the population size is kept constant equal to N > 1, through the following selection mechanism: at all times only the N fittest particles survive, while all the other particles are removed. Fitness is measured with respect to some given score function s : R-d -> R. For some choices of the function s, it is proved that the cloud of particles travels at positive speed in some possibly...
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作者：Mourrat, Jean-Christophe; Valesin, Daniel
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); University of Groningen
摘要：Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with small average graph distance between vertices, but adding an edge comes at a cost measured according to the geometry of the ambient physical space. In most cases, we identify the order of magnitude of the average graph distance as a function of the parameters...
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作者：Angel, Omer; Kolesnik, Brett
作者单位：University of British Columbia; University of California System; University of California Berkeley
摘要：For fixed r >= 2, we consider bootstrap percolation with threshold r on the Erdos-Renyi graph G(n,p). We identify a threshold for p above which there is with high probability a set of size r that can infect the entire graph. This improves a result of Feige, Krivelevich and Reichman, which gives bounds for this threshold, up to multiplicative constants. As an application of our results, we obtain an upper bound for the threshold for K-4-percolation on G(n,p), as studied by Balogh, Bollobas and ...
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作者：Del Moral, P.; Tugaut, J.
作者单位：Universite de Bordeaux
摘要：The ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field McKean-Vlasov-type particle interpretation of the Kalman-Bucy diffusions. In contrast to more conventional particle filters and nonlinear Markov processes, these models are designed in terms of a diffusion process with a diffusion matrix that depends on particle...
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作者：Xu, Liping
作者单位：Sorbonne Universite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a strong/weak stability estimate for the 3D homogeneous Boltzmann equation with moderately soft potentials [gamma epsilon ( -1, 0)] using the Wasserstein distance with quadratic cost. This in particular implies the uniqueness in the class of all weak solutions, assuming only that the initial condition has a finite entropy and a finite moment of sufficiently high order. We also consider the Nanbu N-stochastic particle system, which approximates the weak solution. We use a probabilistic...
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作者：Turova, Tatyana S.
作者单位：Lund University
摘要：We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31-36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3-dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptot...
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作者：Guo, Heng; Jerrum, Mark
作者单位：University of Edinburgh; University of London; Queen Mary University London
摘要：We show that the mixing time of Glauber (single edge update) dynamics for the random cluster model at q = 2 on an arbitrary n-vertex graph is bounded by a polynomial in n. As a consequence, the Swendsen Wang algorithm for the ferromagnetic Ising model at any temperature also has a polynomial mixing time bound.
