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作者：Lee, Sungchul
作者单位：National University of Singapore
摘要：Let {X-i : i >= 1} be i.i.d. with uniform distribution [-1/2, 1/2](d), d >= 2, and let T-n be a minimal spanning tree on {X-1,..., X-n}. For each strictly positive integer alpha, let N({X-1,..., X-n}; alpha) be the number of vertices of degree alpha in T-n. Then, for each alpha such that P(N({X-1,..., X alpha+1}; alpha) = 1. > 0, we prove a central limit theorem for N({X-1,..., X-n}; alpha).
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作者：Durrett, Rick; Neuhauser, Claudia
作者单位：Cornell University; University of Minnesota System; University of Minnesota Twin Cities; University of Wisconsin System; University of Wisconsin Madison
摘要：Barley yellow dwarf is a widespread disease that affects small grains and many grass species, as well as wheat, barley and oat. The disease is caused by an aphid transmitted virus. Rochow conducted a study near Ithaca, New York, which showed that a shift in the dominant strain occurred between 1957 and 1976. Motivated by this phenomenon, we develop a model for the competition between different strains of the barley yellow dwarf virus. Our main goal is to understand the phase diagram of the mod...
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作者：Heath, David; Resnick, Sidney; Samorodnitsky, Gennady
作者单位：Cornell University
摘要：We study the time it takes until a fluid queue with a finite, but large, holding capacity reaches the overflow point. The queue is fed by an on/off process with a heavy tailed on distribution which is known to have long memory. It turns out that the expected time until overflow, as a function of capacity L, increases only polynomially fast; so overflows happen much more often than in the classical light tailed case, where the expected overflow time increases as an exponential function of L. Mo...
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作者：Ball, Frank; Mollison, Denis; Scalia-Tomba, Gianpaolo
作者单位：University of Nottingham; Heriot Watt University; Sapienza University Rome
摘要：We consider epidemics with removal (SIR epidemics) in populations that mix at two levels: global and local. We develop a general modelling framework for such processes, which allows us to analyze the conditions under which a large outbreak is possible, the size of such outbreaks when they can occur and the implications for vaccination strategies, in each case comparing our results with the simpler homogeneous mixing case. More precisely, we consider models in which each infectious individual i...
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作者：Schinazi, Rinaldo B.
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：We consider two interacting particle systems on Z(d) to model predator- prey and host-parasite interactions. In both models we have two types of particles (1 and 2) and each site in Z(d) can be in one of four states: empty, occupied by a type 1 particle, occupied by a type 2 particle or occupied by two particles (one of each type). Each type gives birth to particles of the same type on nearest neighbor sites. The interaction between the two types of particles occurs only when a site is occupie...
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作者：Assaf, David
作者单位：Hebrew University of Jerusalem
摘要：A continuous time Markov chain is observed with Gaussian white noise added to it. To the well-known problem of continuously estimating the current state of the chain, we introduce the additional option of continuously varying the sampling rates, as long as some restriction (or cost) on the average sampling rate is satisfied. The optimal solution to this dynamic sampling problem is presented and analyzed in closed form for the two-state symmetric case. It is shown that the resulting dynamic sam...
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作者：Mathew, Thomas; Nordstrom, Kenneth
作者单位：University System of Maryland; University of Maryland Baltimore County; University of Helsinki
摘要：Let X-i and Y-i follow noncentral chi-square distributions with the same degrees of freedom nu(i) and noncentrality parameters delta(2)(i) and delta(2)(i), respectively, for i = 1, ..., n, and let the Xi's be independent and the Yi's independent. A necessary and sufficient condition is obtained under which Sigma(n)(i=1) lambda(i) X-i is stochastically smaller than Sigma(n)(i=1) lambda(i) Y-i for all nonnegative real numbers lambda(1) >= ... >= lambda(n). Reformulating this as a result in geome...
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作者：Rinott, Yosef; Rotar, Vladimir
作者单位：University of California System; University of California San Diego; Russian Academy of Sciences; Central Economics & Mathematics Institute RAS
摘要：This paper deals with rates of convergence in the CLT for certain types of dependency. The main idea is to combine a modification of a theorem of Stein, requiring a coupling construction, with a dynamic set-up provided by a Markov structure that suggests natural coupling variables. More specifically, given a stationary Markov chain X-(t) and a function U=U(X-(t)), we propose a way to study the proximity of U to a normal random variable when the state space is large. We apply the general method...
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作者：Burton, Robert M.; Faris, William G.
作者单位：Oregon State University; University of Arizona
摘要：The state of the self-organizing cluster process is a finite subset of points in a bounded region. This subset represents an evolving discrete approximation to a continuous probability distribution in the region. The dynamics of the process is determined by an independent sequence of random points in the region chosen according to the distribution. At each time step the random point attracts the nearest point in the finite set. In this way the subset learns to approximate its environment. It i...
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作者：Alexander, Kenneth S.
作者单位：University of Southern California
摘要：We prove a central limit theorem for the length of the minimal spanning tree of the set of sites of a Poisson process of intensity lambda in [0, 1](2) as lambda -> infinity. As observed previously by Ramey, the main difficulty is the dependency between the contributions to this length from different regions of [0, 1](2); a percolation-theoretic result on circuits surrounding a fixed site can be used to control this dependency. We prove such a result via a continuum percolation version of the R...
