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991.
A general theory for random walks on transfinite networks whose ranks are arbitrary natural numbers is established herein. In such networks, nodes of higher ranks connect together transfinite networks of lower ranks. The probabilities for transitions through such nodes are obtained as extensions of the Nash-Williams rule for random walks on ordinary infinite networks. The analysis is based on the theory of transfinite electrical networks, but it requires that the transfinite network have a structure that generalizes local-finiteness for ordinary infinite networks. The shorting together of nodes of different ranks are allowed; this complicates transitions through such nodes but provides a considerably more general theory. It is shown that, with respect to any finite set of nodes of any ranks, a transfinite random walk can be represented by an irreducible reversible Makov chain, whose state space is that set of nodes.This work was supported by the National Science Foundation under the grants DMS-9200738 and MIP-9200748.  相似文献   
992.
Maximally Equidistributed Combined Tausworthe Generators   总被引:4,自引:0,他引:4  
Tausworthe random number generators based on a primitive trinomial allow an easy and fast implementation when their parameters obey certain restrictions. However, such generators, with those restrictions, have bad statistical properties unless we combine them. A generator is called maximally equidistributed if its vectors of successive values have the best possible equidistribution in all dimensions. This paper shows how to find maximally equidistributed combinations in an efficient manner, and gives a list of generators with that property. Such generators have a strong theoretical support and lend themselves to very fast software implementations.

  相似文献   

993.
The Baba and Dorea global minimization methods have been applied to two physical problems. The first one is that of finding the global minimum of the transformer design function of six variables subject to constraints. The second one is the problem of fitting the orbit of a satellite using a set of observations. The latter problem is reduced to that of finding the global minimum of the sum of the squares of the differences between the observed values of the azimuth, elevation, and range at certain intervals of time from the epoch and the computed values of the azimuth, elevation, and range at the same intervals of time. Baba and Dorea established theoretically that the random optimization methods converge to the global minimum with probability one. The numerical experiments carried out for the above two problems show that convergence is very slow for the first problem and is even slower for the second problem. In both cases, it has not been possible to reach the global minimum if the search domains of the variables are wide, even after a very large number of function evaluations.The author thanks the referee for his suggestions on improving the presentation of the paper.  相似文献   
994.
We compute the exact asymptotic normalizations of random walks in random sceneries, for various null recurrent random walks to the nearest neighbours, and for i.i.d., centered and square integrable random sceneries. In each case, the standard deviation grows like n with . Here, the value of the exponent is determined by the sole geometry of the underlying graph, as opposed to previous examples, where this value reflected mainly the integrability properties of the steps of the walk, or of the scenery. For discrete Bessel processes of dimension d[0;2[, the exponent is . For the simple walk on some specific graphs, whose volume grows like nd for d[1;2[, the exponent is =1−d/4. We build a null recurrent walk, for which without logarithmic correction. Last, for the simple walk on a critical Galton–Watson tree, conditioned by its nonextinction, the annealed exponent is . In that setting and when the scenery is i.i.d. by levels, the same result holds with .  相似文献   
995.
The various theoretical considerations for the effects of quenched random fields (RF) on second-order transitions as well as the experimental situation are briefly reviewed. Some of the physical realizations of the RF models are discussed, with an emphasis on solid-state first-order transitions in impure systems. The physical arguments for the RF effects in the bulk as well as on phase interfaces are discussed. In the latter case it is suggested that scattering experiments can probe the details of the interface fluctuations. The role of long relaxation times and metastability in Ising RF systems is emphasized.Research at Tel Aviv University partially supported by the U.S.-Israel Binational Science Foundation (BSF), Jerusalem, Israel.  相似文献   
996.
Module Homomorphisms on Random Normed Modules   总被引:6,自引:0,他引:6  
ModuleHomomorphismsonRandomNormedModulesGuoTiexin(郭铁信)(DepartmentofMathematics,XiamenUniversity,Xiamen,Fujian,361005)Abstract...  相似文献   
997.
998.
Noëlle Pottier   《Physica A》1996,230(3-4):563-576
An analytic study of a one-dimensional biased random walk with correlations between nearest-neighbour steps is presented, both in a lattice model and in its continuous version. First, the treatment of the unbiased problem is recalled and the effect of correlations on the diffusion coefficient is discussed. Then the study is extended to the biased case. The problem is then completely determined by two independent parameters, the degree of correlations in the motion on the one hand and the value of the bias on the other. Both the velocity of the particle and its diffusion coefficient are computed. As a result, the velocity as well as the diffusion coefficient are enhanced when there are positive correlations (qualified as persistence) in the motion, and reduced in the opposite case.  相似文献   
999.
Hema Ramachandran 《Pramana》2002,58(2):313-323
Experimental realization of mirrorless lasers in the last decade have resulted in hectic activity in this field, due to their novelty, simplicity and ruggedness and their great potential for application. In this article, I will review the various developments in this field in roughly chronological order, and discuss some possible applications of this exciting phenomenon, also termed as ‘random lasing’.  相似文献   
1000.
Summary We consider a model of random walk on ℤν, ν≥2, in a dynamical random environment described by a field ξ={ξ t (x): (t,x)∈ℤν+1}. The random walk transition probabilities are taken as P(X t +1= y|X t = x t =η) =P 0( yx)+ c(yx;η(x)). We assume that the variables {ξ t (x):(t,x) ∈ℤν+1} are i.i.d., that both P 0(u) and c(u;s) are finite range in u, and that the random term c(u;·) is small and with zero average. We prove that the C.L.T. holds almost-surely, with the same parameters as for P 0, for all ν≥2. For ν≥3 there is a finite random (i.e., dependent on ξ) correction to the average of X t , and there is a corresponding random correction of order to the C.L.T.. For ν≥5 there is a finite random correction to the covariance matrix of X t and a corresponding correction of order to the C.L.T.. Proofs are based on some new L p estimates for a class of functionals of the field. Received: 4 January 1996/In revised form: 26 May 1997  相似文献   
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