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作者：Balogh, Jozsef; Bollobas, Bela; Krivelevich, Michael; Muller, Tobias; Walters, Mark
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Tel Aviv University; University of Cambridge; University of London
摘要：We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penrose. We also show that in the k-nearest neighbor model, there is a constant. such that almost every kappa-connected graph has a Hamilton cycle.
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作者：Collevecchio, Andrea; Schmitz, Tom
作者单位：Universita Ca Foscari Venezia; Max Planck Society
摘要：We develop a technique that provides a lower bound on the speed of transient random walk in a random environment on regular trees. A refinement of this technique yields upper bounds on the first regeneration level and regeneration time. In particular, a lower and upper bound on the covariance in the annealed invariance principle follows. We emphasize the fact that our methods are general and also apply in the case of once-reinforced random walk. Durrett, Kesten and Limic [Probab. Theory Relate...
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作者：Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and fluctuations of near-geodesics in the network generated by the line process. The notion of a Poissonian city is introduced, in which connections between pairs of nodes are made using simple no-overshoot paths based on the Poisson line process. Asymptotics for geom...
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作者：James, Lancelot F.; Zhang, Zhiyuan
作者单位：Hong Kong University of Science & Technology; Shanghai University of Finance & Economics
摘要：Quantile clocks are defined as convolutions of subordinators L, with quantile functions of positive random variables. We show that quantile clocks can be chosen to be strictly increasing and continuous and discuss their practical modeling advantages as business activity times in models for asset prices. We show that the marginal distributions of a quantile clock, at each fixed time, equate with the marginal distribution of a single subordinator. Moreover, we show that there are many quantile c...
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作者：Pan, G. M.; Zhou, W.
作者单位：Nanyang Technological University; National University of Singapore
摘要：In this paper we prove the central limit theorem for Hotelling's T-2 statistic when the dimension of the random vectors is proportional to the sample size.
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作者：Kardaras, Constantinos
作者单位：Boston University
摘要：We provide an axiomatic foundation for the representation of numeraire-invariant preferences of economic agents acting in a financial market. In a static environment, the simple axioms turn out to be equivalent to the following choice rule: the agent prefers one outcome over another if and only if the expected (under the agent's subjective probability) relative rate of return of the latter outcome with respect to the former is nonpositive. With the addition of a transitivity requirement, this ...
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作者：Bramson, Maury
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：There has recently been considerable interest in the stability of different fair bandwidth sharing policies for models that arise in the context of Internet congestion control. Here, we consider a connection level model, introduced by Massoulie and Roberts [Telecommunication Systems 15 (2000) 185-201], that represents the randomly varying number of flows present in a network. The weighted alpha-fair and weighted max-min fair bandwidth sharing policies are among important policies that have bee...
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作者：Kim, Jeong Han; Montenegro, Ravi; Peres, Yuval; Tetali, Prasad
作者单位：Yonsei University; National Institute for Mathematical Sciences (NIMS), Republic of Korea; Microsoft; University of Massachusetts System; University of Massachusetts Lowell; University System of Georgia; Georgia Institute of Technology
摘要：We show a Birthday Paradox for self-intersections of Markov chains with uniform stationary distribution. As an application, we analyze Pollard's Rho algorithm for finding the discrete logarithm in a cyclic group G and find that if the partition in the algorithm is given by a random oracle, then with high probability a collision occurs in Theta(root vertical bar G vertical bar) steps. Moreover, for the parallelized distinguished points algorithm on J processors we find that Theta(root vertical ...
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作者：Santos, Manuel S.
作者单位：University of Miami; Universidad Carlos III de Madrid
摘要：This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions indexed by a vector of parameters. A key step in the method of proof is to show the uniform convergence (a.s.) of a family of sample distributions over the domain of parameters. This uniform convergence holds under mild continuity and monotonicity conditions on...
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作者：Deaconu, Madalina; Lejay, Antoine
作者单位：Inria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine
摘要：The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with importance sampling techniques. The first interest of this approach is that the weights can be easily computed from the density of the one-dimensional Brownian motion. Compared to the Euler scheme this method allows one to obtain a more accurate approximation ...
