The asymptotic behavior of elementary symmetric functions on a probability distribution

On the Balanced Elementary Symmetric Boolean Functions

or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. SUMMARY In this paper, we give some results towards the conject...

On the elementary symmetric functions of a sum of matrices

Often in mathematics it is useful to summarize a multivariate phenomenon with a single number. In fact, the determinant – which is denoted by det – is one of the simplest cases and many of its properties are very well-known. For instance, the determinant is a multiplicative function, i.e. det(AB) = detA · detB, A,B ∈ Mn, and it is a multilinear function, but it is not, in general, an additive f...

On the Concavity of Multivariate Probability Distribution Functions on the Concavity of Multivariate Probability Distribution Functions

We prove that the multivariate standard normal probability distribution function is concave for large argument values. The method of proof allows for the derivation of similar statements for other types of multivariate probability distribution functions too. The result has important application, e.g., in probabilistic constrained stochastic programming problems.

Asymptotic estimates of elementary probability distributions

Several new asymptotic estimates (with precise error bounds) are derived for Poisson and binomial distributions as the parameters tend to infinity. The analytic methods used are also applicable to other discrete distribution functions. AMS 1991 Mathematical Subject Classification: 60A99 33B20.

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions