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作者：PITTEL, B
摘要：In a set of even cardinality n, each member ranks all the others in order of preference. A stable matching is a partition of the set into n/2 pairs, with the property that no two unpaired members both prefer each other to their partners under matching. It is known that for some problem instances no stable matching exists. What if an instance of the ranking system is chosen uniformly at random? We show that the mean and the variance of the total number of stable matchings for the random problem...
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作者：CHANG, FC; KEMPERMAN, JHB; STUDDEN, WJ
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：Let LAMBDA be the set of probability measures lambda on [0, 1]. Let M(n) = {(c1,..., c(n))\lambda is-an-element-of LAMBDA), where c(k) = c(k)(lambda) = integral-1/0x(k) dlambda, k = 1, 2,... are the ordinary moments, and assign to the moment space M(n) the uniform probability measure P(n). We show that, as n --> infinity, the fixed section (c1,..., c(k)), properly normalized, is asymptotically normally distributed. That is, square-root n[(c1,..., c(k)) - (c1(0),..., c(k)0] converges to MVN(0, ...
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作者：KRONE, SM
作者单位：University of Massachusetts System; University of Massachusetts Amherst
摘要：In this work we study local times for a class of measure-valued Markov processes known as superprocesses. We begin by deriving analogues of well-known properties of ordinary local times. Then, restricting our attention to a class of superprocesses (which includes the important case of super-Brownian motion), we prove more detailed properties of the local times, such as joint continuity and a global Holder condition. These are then used to obtain path properties of the superprocesses themselves...
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作者：CHAGANTY, NR; SETHURAMAN, J
作者单位：State University System of Florida; Florida State University
摘要：Most large deviation results give asymptotic expressions for log P(Y(n) greater-than-or-equal-to y(n)), where the event {Y(n) greater-than-or-equal-to y(n)) is a large deviation event, that is, P(Y(n) greater-than-or-equal-to y(n)) goes to 0 exponentially fast. We refer to such results as weak large deviation results. In this paper we obtain strong large deviation results for arbitrary random variables {Y(n)}, that is, we obtain asymptotic expressions for P(Y(n) greater-than-or-equal-to y(n)),...
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作者：CAI, HY; LUO, XL
作者单位：Cornell University
摘要：We prove laws of large numbers for a cellular automaton in the space {0,1,..., p - 1}Z with p being a prime number. The dynamics tau of the system are defined by taueta(x) = eta(x - 1) + eta(x + 1) mod p for eta is-an-element-of X.
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作者：ETHIER, SN; GRIFFITHS, RC
作者单位：Monash University
摘要：Let S be a compact metric space, let theta greater-than-or-equal-to 0, and let nu0 be a Borel probability measure on S. An explicit formula is found for the transition function of the Fleming-Viot process with type space S and mutation operator (Af)(x) = (1/2)theta integral(S)(f(xi) - f(x))nu0(dxi).
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作者：RIO, E
摘要：Let (X(i))i is-an-element-of Z(+)d be an array of zero-mean independent identically distributed random vectors with values in R(k) with finite variance, and let J be a class of Borel subsets of [0, 1]d. If, for the usual metric, J is totally bounded and has a convergent entropy integral, we obtain a strong invariance principle for an appropriately smoothed version of the partial-sum process {SIGMA(i is-an-element-of nu S)X(i): S is-an-element-of J} with an error term depending only on J and on...
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作者：EISENBAUM, N; KASPI, H
作者单位：Technion Israel Institute of Technology
摘要：Let X be a Markov process on an interval E of R, with lifetime zeta, admitting a local time at each point and such that P(x)(X hits y) > 0 for all x, y in E. We prove here that the local times process (L(zeta)x, x is-an-element-of E) is a Markov process if and only if X has fixed birth and death points and X has continuous paths. The sufficiency of this condition has been established by Ray, Knight and Walsh. The necessity is proved using arguments based on excursion theory. This result has be...
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作者：FALK, M; MAROHN, F
摘要：It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an iid sample, whether in terms of the distribution of the largest order ...
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作者：FONTES, LRG
摘要：For continuum 1/r2 Ising models, we prove that the critical value of the long range coupling constant (inverse temperature), above which an ordered phase occurs (for strong short range cutoff), is exactly 1. This leads to a proof of the existence of an ordered phase with slow decay of correlations. Our arguments involve comparisons between continuum and discrete Ising models, including (quenched and annealed) site diluted models, which may be of independent interest.
