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51.
Lutz Mattner 《Probability Theory and Related Fields》2004,130(2):151-166
This is a contribution to the theory of sums of independent random variables at an algebraico-analytical level: Let Prob denote the convolution semigroup of all probability measures on with all moments finite, topologized by polynomially weighted total variation. We prove that the cumulant sequence regarded as a function from Prob into the additive topological group ofall real sequences, is universal among continuous homomorphisms from Prob into Hausdorff topological groups, in the usual sense that every other such homomorphism factorizes uniquely through . An analogous result, referring to just the first cumulants,holds for the semigroup of all probability measures with existing rth moments. In particular, there is no nontrivial continuous homomorphism from the convolution semigroup of all probability measures, topologized by the total variation metric, into any Hausdorff topological group.Mathematics Subject Classification (2000): 60B15, 60E10, 60G50 相似文献
52.
Endre Boros Khaled Elbassioni Vladimir Gurvich Leonid Khachiyan 《Mathematical Programming》2003,98(1-3):355-368
A result of Balas and Yu (1989) states that the number of maximal independent sets of a graph G is at most p+1, where is the number of pairs of vertices in G at distance 2, and p is the cardinality of a maximum induced matching in G. In this paper, we give an analogue of this result for hypergraphs and, more generally, for subsets of vectors in the product of n lattices =1××n, where the notion of an induced matching in G is replaced by a certain binary tree each internal node of which is mapped into . We show that our bounds may be nearly sharp for arbitrarily large hypergraphs and lattices. As an application, we prove that the number of maximal infeasible vectors x=1××n for a system of polymatroid inequalities does not exceed max{Q,logt/c(2Q,)}, where is the number of minimal feasible vectors for the system, , , and c(,) is the unique positive root of the equation 2c(c/log–1)=1. This bound is nearly sharp for the Boolean case ={0,1}n, and it allows for the efficient generation of all minimal feasible sets to a given system of polymatroid inequalities with quasi-polynomially bounded right-hand sides .
This research was supported by the National Science Foundation (Grant IIS-0118635), and by the Office of Naval Research (Grant N00014-92-J-1375). The second and third authors are also grateful for the partial support by DIMACS, the National Science Foundation's Center for Discrete Mathematics and Theoretical Computer Science.Mathematics Subject Classification (2000):20E28, 20G40, 20C20 相似文献
53.
We address the problem of finding the worst possible traffic a
user of a telecommunications network can send.
We take worst to mean having the highest effective
bandwidth, a concept that arises in the Large Deviation theory of
queueing networks.
The traffic is assumed to be stationary and to satisfy leaky bucket
constraints, which represent the a priori knowledge the network
operator has concerning the traffic.
Firstly, we show that this optimization problem may be reduced to an
optimization over periodic traffic sources.
Then, using convexity methods, we show that the realizations of a
worst case source must have the following properties:
at each instant the transmission rate must be either zero,
the peak rate, or the leaky bucket rate; it may only be the latter when
the leaky bucket is empty or full;
each burst of activity must either start with the leaky
bucket empty or end with it full. 相似文献
54.
J. Sunklodas 《Lithuanian Mathematical Journal》2001,41(3):292-305
We derive lower bounds for Lp norms
, in the central limit theorem for independent and m–dependent random variables with finite fifth order absolute moments and for independent and m–dependent identically distributed random variables with fourth order moments. 相似文献
55.
Hongbin Zhang 《International Journal of Infrared and Millimeter Waves》2007,28(9):713-723
A spatially independent model of vertical-cavity surface-emitting lasers (VCSELs) is derived by integrating the spatially
dependent rate equations over the cross section of the cavity of a VCSEL. The angular and radial non-uniformities of the injection
current are taken into account. The well-known LP modes of a weakly-guiding cylindrical waveguide are employed to describe
the transverse modal structure in the VCSEL cavity. This model is solved in a self-consistent way by using the 4th order Runge-Kutta
method. The dependence of transverse mode competition on the current intensity, the angular and radial non-uniformities of
the injection current, and the geometrical parameters of the electrical contact are thoroughly investigated and analyzed.
The results are useful to the optimum design of the optical transverse modal structure of VCSELs. 相似文献
56.
Michał Dobrski 《Central European Journal of Physics》2007,5(3):313-323
In this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by
canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time
independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian
for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.
相似文献
57.
We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show that the Glauber dynamics for proper q‐colorings of a hypergraph mixes rapidly if m ≥ 4 and q > Δ, and if m = 3 and q ≥ 1.65Δ. We give related results on the hardness of exact and approximate counting for both problems. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 相似文献
58.
In 1952 Darling proved the limit theorem for the sums of independent identically distributed random variables without power moments under the functional normalization. This paper contains an alternative proof of Darling’s theorem, using the Laplace transform. Moreover, the asymptotic behavior of probabilities of large deviations is studied in the pattern under consideration. 相似文献
59.
60.
Yu. A. Dabaghian 《Theoretical and Mathematical Physics》2008,156(1):996-1019
We discuss how to obtain exact and approximate distributions for various statistical characteristics of the spectra of quantum
graphs using previously found exact solutions of the spectral problem. We indicate the relation between the appearing spectral
decompositions and the theory of weakly dependent random variables and indicate the relation between the known limit theorems
for trigonometric sums and the universal statistical properties of the spectra of quantum chaotic systems.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 1, pp. 38–66, July, 2008. 相似文献