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作者：Ellis, Richard S.; Machta, Jonathan; Otto, Peter Tak-Hun
作者单位：University of Massachusetts System; University of Massachusetts Amherst; University of Massachusetts System; University of Massachusetts Amherst; Willamette University
摘要：The main focus of this paper is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume-Capel model. We show that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter alpha governing the speed ...
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作者：Limic, Vlada; Volkov, Stanislav
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; University of Bristol
摘要：By a theorem of Volkov [12] we know that on most graphs with positive probability the linearly vertex-reinforced random walk (VRRW) stays within a finite trapping subgraph at all large times. The question of whether this tail behavior occurs with probability one is open in general. In his thesis, Pemantle [5] proved, via a dynamical system approach, that for a VRRW on any complete graph the asymptotic frequency of visits is uniform over vertices. These techniques do not easily extend even to t...
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作者：Ding, Xue; Jiang, Tiefeng
作者单位：Jilin University; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the Laplacian matrices; (ii) under some further independent conditions, the normalized largest eigenvalues of the Laplacian matrices are dense in a compact interval almost surely; (iii) the empirical distributions of the eigenvalues of the Laplacian matrices converg...
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作者：Bertoin, Jean
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are interested in asymptotics of the partition of the total population into colonies for large populations with rare migrations. Under appropriate regimes, we establish weak convergence of the rescaled partition to some random measure that is constructed from the restriction of a Poisson point measure to a ce...
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作者：Elskens, Yves; Pardoux, Etienne
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：The one-dimensional motion of any number N of particles in the field of many independent waves (with strong spatial correlation) is formulated as a second-order system of stochastic differential equations, driven by two Wiener processes. In the limit of vanishing particle mass m -> 0, or, equivalently, of large noise intensity, we show that the momenta of all N particles converge weakly to N independent Brownian motions, and this convergence holds even if the noise is periodic. This justifies ...
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作者：Saksman, Eero; Vihola, Matti
作者单位：University of Helsinki; University of Jyvaskyla
摘要：This paper describes sufficient conditions to ensure the correct ergodicity of the Adaptive Metropolis (AM) algorithm of Haario, Saksman and Tamminen [Bernoulli 7 (2001) 223-242] for target distributions with a noncompact support. The conditions ensuring a strong law of large numbers require that the tails of the target density decay super-exponentially and have regular contours. The result is based on the ergodicity of an auxiliary process that is sequentially constrained to feasible adaptati...
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作者：Bordenave, Charles; Torrisi, Giovanni Luca
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Rome Tor Vergata; Consiglio Nazionale delle Ricerche (CNR); Istituto per le Applicazioni del Calcolo Mauro Picone (IAC-CNR)
摘要：We analyze the asymptotic properties of a Euclidean optimization problem on the plane. Specifically, we consider a network with three bins and n objects spatially uniformly distributed, each object being allocated to a bin at a cost depending on its position. Two allocations are considered: the allocation minimizing the bin loads and the allocation allocating each object to its less costly bin. We analyze the asymptotic properties of these allocations as the number of objects grows to infinity...
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作者：Krieger, Abba M.; Pollak, Moshe; Samuel-Cahn, Ester
作者单位：University of Pennsylvania; Hebrew University of Jerusalem
摘要：The present paper studies the limiting behavior of the average score of a sequentially selected group of items or individuals, the underlying distribution of which, F, belongs to the Gumbel domain of attraction of extreme value distributions. This class contains the Normal, Lognormal, Gamma, Weibull and many other distributions. The selection rules are the better than average (beta = 1) and the beta-better than average rule, defined as follows. After the first item is selected, another item is...
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作者：Doku-Amponsah, Kwabena; Moerters, Peter
作者单位：University of Ghana; University of Bath
摘要：For any finite colored graph we define the empirical neighborhood measure, which counts the number of vertices of a given color connected to a given number of vertices of each color, and the empirical pair measure, which counts the number of edges connecting each pair of colors. For a class of models of sparse colored random graphs, we prove large deviation principles for these empirical measures in the weak topology. The rate functions governing our large deviation principles can be expressed...
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作者：Kang, Weining; Ramanan, Kavita
作者单位：University System of Maryland; University of Maryland Baltimore County; Brown University
摘要：This work considers a many-server queueing system in which impatient customers with i.i.d., generally distributed service times and i.i.d., generally distributed patience times enter service in the order of arrival and abandon the queue if the time before possible entry into service exceeds the patience time. The dynamics of the system is represented in terms of a pair of measure-valued processes, one that keeps track of the waiting times of the customers in queue and the other that keeps trac...
