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作者：Jahnel, Benedikt; Kuelske, Christof
作者单位：Ruhr University Bochum
摘要：We consider a class of discrete q-state spin models defined in terms of a translation-invariant quasilocal specification with discrete clock-rotation invariance which have extremal Gibbs measures mu(1)(phi) labeled by the uncountably many values of phi in the one-dimensional sphere (introduced by van Enter, Opoku, Kulske [J. Phys. A 44 (2011) 475002, 11]). In the present paper we construct an associated Markov jump process with quasilocal rates whose semigroup (S-t)(t >= 0) acts by a continuou...
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作者：Gurvich, Itai
作者单位：Northwestern University
摘要：Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove, approximates that of the Markov chain with notable. precision. Strong approximations provide such limitless approximations for process dynamics. Our focus here is on steady-state distributions, and the diffusion model that we propose is tractable relative to ...
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作者：Khandwawala, Mustafa; Sundaresan, Rajesh
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：We apply the objective method of Aldous to the problem of finding the minimum-cost edge cover of the complete graph with random independent and identically distributed edge costs. The limit, as the number of vertices goes to infinity, of the expected minimum cost for this problem is known via a combinatorial approach of Hessler and Wastlund. We provide a proof of this result using the machinery of the objective method and local weak convergence, which was used to prove the (2) limit of the ran...
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作者：Chafai, Djalil; Gozlan, Nathael; Zitt, Pierre-Andre
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel
摘要：We study a physical system of N interacting particles in R-d, d >= 1, subject to pair repulsion and confined by an external field. We establish a large deviations principle for their empirical distribution as N tends to infinity. In the case of Riesz interaction, including Coulomb interaction in arbitrary dimension d > 2, the rate function is strictly convex and admits a unique minimum, the equilibrium measure, characterized via its potential. It follows that almost surely, the empirical distr...
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作者：Addario-Berry, Louigi; Broutin, Nicolas; Holmgren, Cecilia
作者单位：McGill University; Stockholm University
摘要：We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galton-Watson tree with critical, finite-variance offspring distribution, conditioned to have total progeny n. Our proof is based on a coupling which yields a precise, nonasymptotic distributional result for the case of uniformly random rooted labeled trees (or, equivalently, Poisson Galton-Watson trees conditioned on their size). Our approach also provides a new, random reversible transfo...
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作者：Shah, D.; Walton, N. S.; Zhong, Y.
作者单位：Massachusetts Institute of Technology (MIT); University of Amsterdam; Columbia University
摘要：We consider a switched (queuing) network in which there are constraints on which queues may be served simultaneously; such networks have been used to effectively model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time, based on the current state or past history of the system. In the main result of this paper, we provide a new class of online scheduling policies that achieve optimal queue-size scaling for a...
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作者：Hairer, Martin; Stuart, Andrew M.; Vollmer, Sebastian J.
作者单位：University of Warwick
摘要：We study the problem of sampling high and infinite dimensional target measures arising in applications such as conditioned diffusions and inverse problems. We focus on those that arise from approximating measures on Hilbert spaces defined via a density with respect to a Gaussian reference measure. We consider the Metropolis Hastings algorithm that adds an accept reject mechanism to a Markov chain proposal in order to make the chain reversible with respect to the target measure. We focus on cas...
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作者：Peskir, Goran
作者单位：University of Manchester
摘要：Let Z = (Z(t))(t >= 0) be a regular diffusion process started at 0, an independent random variable with a strictly increasing and continue:.stribution function F, and let tau(l) = inf{t >= 0 vertical bar Z(t) = l} be the first entry, ... of Z at the level l. We show that the quickest detection problem tau sup E[R-tau - (0)integral(tau) c(R-t) dt], where R = S I is the range process of X = 2F(Z) 1 (i.e., the difference between the running maximum and the running minimum of X) and c(r) = cr with...
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作者：Podolskij, Mark; Schmidt, Christian; Ziegel, Johanna F.
作者单位：Ruprecht Karls University Heidelberg; University of Bern
摘要：This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Ito semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.
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作者：Broniatowski, Michel; Caron, Virgile
作者单位：Sorbonne Universite
摘要：This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a function of its summands as their number tends to infinity. In the large deviation range of the conditioning event it extends the Gibbs conditional principle in the sense that it provides a description of the distribution of the random walk on long subsequences. An approximation of the density of the runs is also obtained when the conditioning event states t...
