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1.
We study the higher-order correlation functions of covariant families of observables associated with random Schr?dinger operators
on the lattice in the strong disorder regime. We prove that if the distribution of the random variables has a density analytic
in a strip about the real axis, then these correlation functions are analytic functions of the energy outside of the planes
corresponding to coincident energies. In particular, this implies the analyticity of the density of states, and of the current-current
correlation function outside of the diagonal. Consequently, this proves that the current-current correlation function has
an analytic density outside of the diagonal at strong disorder.
Submitted: October 8, 2005; Accepted: February 15, 2006 相似文献
2.
Tail distribution bounds play a major role in the estimation of failure probabilities in performance and reliability analysis of systems. They are usually estimated using Markov's and Chebyshev's inequalities, which represent tail distribution bounds for a random variable in terms of its mean or variance. This paper presents the formal verification of Markov's and Chebyshev's inequalities for discrete random variables using a higher‐order‐logic theorem prover. The paper also provides the formal verification of mean and variance relations for some of the widely used discrete random variables, such as Uniform(m), Bernoulli(p), Geometric(p) and Binomial(m, p) random variables. This infrastructure allows us to precisely reason about the tail distribution properties and thus turns out to be quite useful for the analysis of systems used in safety‐critical domains, such as space, medicine or transportation. For illustration purposes, we present the performance analysis of the coupon collector's problem, a well‐known commercially used algorithm. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
3.
Feng Qi 《Proceedings Mathematical Sciences》2017,127(4):551-564
In this paper, we present derivatives of the generating functions for the Bell numbers by induction and by the Faà di Bruno formula, recover an explicit formula in terms of the Stirling numbers of the second kind, find the (logarithmically) absolute and complete monotonicity of the generating functions, and construct some inequalities for the Bell numbers. From these inequalities, we derive the logarithmic convexity of the sequence of the Bell numbers. 相似文献
4.
《随机分析与应用》2013,31(4):1009-1025
Abstract In a recent work of the second named author on the Almost Sure Central Limit Theorem (ASCLT), we showed the usefulness of the concept of quasi-orthogonal system of random variables introduced by Bellman and later developed by Kac, Salem and Zygmund. In this paper, we propose an optimal formulation of the ASCLT again by using this idea and new correlation inequalities for sums of independent random variables. We also introduce and develop the notion of “intersective ASCLT” by proving some new results generalizing and improving substancially the classical formulation of the ASCLT. Essential tools for this approach are correlation inequalities recently developed by the first named author and some extensions of these ones obtained in the present paper. 相似文献
5.
A new notion of partition‐determined functions is introduced, and several basic inequalities are developed for the entropies of such functions of independent random variables, as well as for cardinalities of compound sets obtained using these functions. Here a compound set means a set obtained by varying each argument of a function of several variables over a set associated with that argument, where all the sets are subsets of an appropriate algebraic structure so that the function is well defined. On the one hand, the entropy inequalities developed for partition‐determined functions imply entropic analogues of general inequalities of Plünnecke‐Ruzsa type. On the other hand, the cardinality inequalities developed for compound sets imply several inequalities for sumsets, including for instance a generalization of inequalities proved by Gyarmati, Matolcsi and Ruzsa (2010). We also provide partial progress towards a conjecture of Ruzsa (2007) for sumsets in nonabelian groups. All proofs are elementary and rely on properly developing certain information‐theoretic inequalities. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 399–424, 2012 相似文献
6.
Wiesława T. Obuchowska 《Journal of Global Optimization》2010,46(3):423-433
In this paper we investigate certain aspects of infeasibility in convex integer programs, where the constraint functions are
defined either as a composition of a convex increasing function with a convex integer valued function of n variables or the sum of similar functions. In particular we are concerned with the problem of an upper bound for the minimal
cardinality of the irreducible infeasible subset of constraints defining the model. We prove that for the considered class
of functions, every infeasible system of inequality constraints in the convex integer program contains an inconsistent subsystem
of cardinality not greater than 2
n
, this way generalizing the well known theorem of Scarf and Bell for linear systems. The latter result allows us to demonstrate
that if the considered convex integer problem is bounded below, then there exists a subset of at most 2
n
−1 constraints in the system, such that the minimum of the objective function subject to the inequalities in the reduced subsystem,
equals to the minimum of the objective function over the entire system of constraints. 相似文献
7.
Mark Veraar 《Potential Analysis》2009,30(4):341-370
In this paper we extend certain correlation inequalities for vector-valued Gaussian random variables due to Kolmogorov and Rozanov. The inequalities are applied to sequences of Gaussian random variables and Gaussian processes. For sequences of Gaussian random variables satisfying a correlation assumption, we prove a Borel-Cantelli lemma, maximal inequalities and several laws of large numbers. This extends results of Be?ka and Ciesielski and of Hytönen and the author. In the second part of the paper we consider a certain class of vector-valued Gaussian processes which are α-Hölder continuous in p-th moment. For these processes we obtain Besov regularity of the paths of order α. We also obtain estimates for the moments in the Besov norm. In particular, the results are applied to vector-valued fractional Brownian motions. These results extend earlier work of Ciesielski, Kerkyacharian and Roynette and of Hytönen and the author. 相似文献
8.
V. A. Andreev 《Theoretical and Mathematical Physics》2007,152(3):1286-1298
We use the reduced density matrix of the two-particle spin state to construct a generalized Bell-Clauser-Horne-Shimony-Holt
inequality. For each specific state and under a special choice of the vectors
, this inequality becomes an exact equality. We show how such vectors can be found using the reduced density matrix. Both
sides of this equality have a specific numerical value. We indicate the connection of this number with the measure of entanglement
of the two-particle spin state.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 488–501, September, 2007. 相似文献
9.
Yu. P. Virchenko 《Ukrainian Mathematical Journal》1998,50(6):870-878
We consider models of statistical mechanics of the type of lattice gas with attractive interaction of general kind. We propose
a method for obtaining inequalities that connect multipoint correlation functions of different order. This method allows one,
on the one hand, to strengthen similar inequalities, which can be obtained within the framework of the FKG method, and on
the other hand, to obtain new inequalities. We introduce the notion of duality for models of lattice gas. We show that if,
under the transformation p ⇒ 1 - p, the correlation inequalities for a model with attraction turn into the corresponding inequalities that are also satisfied,
then the correlation functions of the dual model also satisfy the latter inequalities.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 765–773, June, 1998. 相似文献
10.
Amitabh Basu Manoel Campêlo Michele Conforti Gérard Cornuéjols Giacomo Zambelli 《Mathematical Programming》2013,141(1-2):561-576
This paper contributes to the theory of cutting planes for mixed integer linear programs (MILPs). Minimal valid inequalities are well understood for a relaxation of an MILP in tableau form where all the nonbasic variables are continuous; they are derived using the gauge function of maximal lattice-free convex sets. In this paper we study lifting functions for the nonbasic integer variables starting from such minimal valid inequalities. We characterize precisely when the lifted coefficient is equal to the coefficient of the corresponding continuous variable in every minimal lifting (This result first appeared in the proceedings of IPCO 2010). The answer is a nonconvex region that can be obtained as a finite union of convex polyhedra. We then establish a necessary and sufficient condition for the uniqueness of the lifting function. 相似文献
11.
Some lower bounds for the variance of a function g of a random vector X are extended to a wider class of distributions. Using these bounds, some useful inequalities for the Fisher information are obtained for convolutions and linear combinations of random variables. Finally, using these inequalities, simple proofs are given of classical characterizations of the normal distribution, under certain restrictions, including the matrix analogue of the Darmois-Skitovich result. 相似文献
12.
Certain constructions of copulas can be interpreted as an eigendecomposition of a kernel. We study some properties of the eigenfunctions and their integrals of a covariance kernel related to a bivariate distribution. The covariance between functions of random variables in terms of the cumulative distribution function is used. Some bounds for the trace of the kernel and some inequalities for a continuous random variable concerning a function and its derivative are obtained. We also obtain relations to diagonal expansions and canonical correlation analysis and, as a by-product, series of constants for some particular distributions. 相似文献
13.
Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications 总被引:1,自引:0,他引:1
In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively
associated random variables, which extend the corresponding results for negatively associated random variables. As applications
of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability,
we derive some results on L
p convergence where 1 < p < 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial
sums of identically distributed random variables. 相似文献
14.
15.
In this article, the authors discuss the L 1-convergence for weighted sums of some dependent random variables under the condition of h-integrability with respect to an array of weights. The dependence structure of the random variables includes pairwise lower case negative dependence and conditions on the mixing coefficient, the maximal correlation coefficient, or the ρ*-mixing coefficient. They prove that all the weighted sums have similar limiting behaviour. 相似文献
16.
《数学季刊》2014,(2)
Some probability inequalities are established for extended negatively dependent(END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results. 相似文献
17.
Farida Kachapova Ilias Kachapov 《International Journal of Mathematical Education in Science & Technology》2013,44(3):418-427
This note introduces a monotony coefficient as a new measure of the monotone dependence in a two-dimensional sample. Some properties of this measure are derived. In particular, it is shown that the absolute value of the monotony coefficient for a two-dimensional sample is between |r| and 1, where r is the Pearson's correlation coefficient for the sample; that the monotony coefficient equals 1 for any monotone increasing sample and equals ?1 for any monotone decreasing sample. This article contains a few examples demonstrating that the monotony coefficient is a more accurate measure of the degree of monotone dependence for a non-linear relationship than the Pearson's, Spearman's and Kendall's correlation coefficients. The monotony coefficient is a tool that can be applied to samples in order to find dependencies between random variables; it is especially useful in finding couples of dependent variables in a big dataset of many variables. Undergraduate students in mathematics and science would benefit from learning and applying this measure of monotone dependence. 相似文献
18.
From the ordinary notion of negative association for a sequence of random variables, a new concept called conditional negative
association is introduced. The relation between negative association and conditional negative association is answered, that
is, the negative association does not imply the conditional negative association, and vice versa. The basic properties of
conditional negative association are developed, which extend the corresponding ones under the non-conditioning setup. By means
of these properties, some Rosenthal type inequalities for maximum partial sums of such sequences of random variables are derived,
which extend the corresponding results for negatively associated random variables. As applications of these inequalities,
some conditional mean convergence theorems, conditionally complete convergence results and a conditional central limit theorem
stated in terms of conditional characteristic functions are established. In addition, some lemmas in the context are of independent
interest. 相似文献
19.
《随机分析与应用》2013,31(6):1177-1189
New very general univariate and multivariate probabilistic Ostrowski type inequalities are established, involving ‖·‖∞ and ‖·‖ p , p≥1 norms of probability density functions. Some of these inequalities provide pointwise estimates to the error of probability distribution function from the expectation of some simple function of the engaged random variable. Other inequalities give upper bounds for the expectation and variance of a random variable. All are done over finite domains. At the end are given applications, especially for the Beta random variable. 相似文献
20.
We derive the Bell–Clauser–Horne–Shimony–Holt inequalities for two-particle mixed spin states both in the conventional quantum mechanics and in the hidden-variables theory. We consider two cases for the vectors
, and
specifying the axes onto which the particle spins of a correlated pair are projected. In the first case, all four vectors lie in the same plane, and in the second case, they are oriented arbitrarily. We compare the obtained inequalities and show that the difference between the predictions of the two theories is less for mixed states than for pure states. We find that the inequalities obtained in quantum mechanics and the hidden-variables theory coincide for some special states, in particular, for the mixed states formed by pure factorable states. We discuss the points of similarity and difference between the uncertainty relations and Bell's inequalities. We list all the states for which the right-hand side of the Bell–Clauser–Horne–Shimony–Holt inequality is identically equal to zero. 相似文献