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作者：Bérard, J
作者单位：Universite Claude Bernard Lyon 1
摘要：We study the asymptotic behavior of two mutation-selection genetic algorithms in random environments. First, the state space is a supercritical Galton-Watson tree conditioned upon non-extinction and the objective function is the distance from the root. In the second case, the state space is a regular tree and the objective function is a sample of a tree-indexed random walk. We prove that, after n steps, the algorithms find the maximum possible value of the objective function up to a finite ran...
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作者：Häggström, O
作者单位：Chalmers University of Technology
摘要：Let X-0,X-1,... be a geometrically ergodic Markov chain with state space X and stationary distribution pi. It is known that if h:X -> R satisfies pi(vertical bar h vertical bar(2+epsilon)) < infinity for some epsilon > 0, then the normalized sums of the X-i's obey a central limit theorem. Here we show, by means of a counterexample, that the condition pi(vertical bar h vertical bar(2+epsilon)) < infinity cannot be weakened to only assuming a finite second moment, i.e., pi(h(2)) < infinity.
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作者：Aldous, D; Miermont, G; Pitman, J
作者单位：University of California System; University of California Berkeley; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite numbe...
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作者：Zerner, MPW
作者单位：Eberhard Karls University of Tubingen
摘要：We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which depends on the environment at that site and on how often the walker has visited that site before. We give exact criteria for recurrence and transience and consider the speed of the walk.
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作者：Graham, C
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We consider N single server infinite buffer queues with service rate beta. Customers arrive at rate Nalpha, choose L queues uniformly, and join the shortest. We study the processes t is an element of R+ (bar right arrow) R-t(N) = (R-t(N)(k))(kis an element ofN) for large N, where R-t(N)(k) is the fraction of queues of length at least k at time t. Laws of large numbers (LLNs) are known, see Vvedenskaya et al. [15], Mitzenmacher [12] and Graham [5]. We consider certain Hilbert spaces with the we...
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作者：Doney, RA; Maller, RA
作者单位：University of Manchester; Australian National University; Australian National University
摘要：We establish an integral test involving only the distribution of the increments of a random walk S which determines whether lim sup(n-->infinity() S-n/n(k)) is almost surely zero, finite or infinite when 1/2 < k < 1 and a typical step in the random walk has zero mean. This completes the results of Kesten and Maller [9] concerning finiteness of one-sided passage times over power law boundaries, so that we now have quite explicit criteria for all values of k >= 0. The results, and those of [9], ...
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作者：Clark, JMC; Crisan, D
作者单位：Imperial College London; Imperial College London
摘要：The paper is concerned with completing unfinished business on a robust representation formula for the conditional expectation operator of nonlinear filtering. Such a formula, robust in the sense that its dependence on the process of observations is continuous, was stated in [2] without proof. The main purpose of this paper is to repair this deficiency. The formula is almost obvious as it can be derived at a formal level by a process of integration-by-parts applied to the stochastic integrals t...
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作者：Breuillard, E
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study the speed of convergence of n(d/2) integral fd mu(*n) in the local limit theorem on R-d under very general conditions upon the function f and the distribution mu. We show that this speed is at least of order 1/n and we give a simple characterization (in diophantine terms) of those measures for which this speed (and the full local Edgeworth expansion) holds for smooth enough f. We then derive a uniform local limit theorem for moderate deviations under a mild moment assumption. This in ...
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作者：Forrester, PJ; Rains, EM
作者单位：University of Melbourne; AT&T
摘要：Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two classical ensembles with orthogonal symmetry and the eigenvalue PDF for a single classical ensemble with unitary symmetry, while the other interpolates between a classical ensemble with orthogonal symmetry and a classical ensemble with symplectic symmetry. We...
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作者：Jiang, TF
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Let Gamma(n)=(gamma(ij)) be an nxn random matrix such that its distribution is the normalized Haar measure on the orthogonal group O(n). Let also W-n:=max(1less than or equal toi,jless than or equal ton)|gamma(ij)|. We obtain the limiting distribution and a strong limit theorem on W-n. A tool has been developed to prove these results. It says that up to n/(log n)(2) columns of Gamma(n) can be approximated simultaneously by those of some Y-n=(y(ij)) in which y(ij) are independent standard norma...
