On a multivariate normal probability minimization problem

Multivariate normal approximation in geometric probability

x ξxδx where the sum is over points x of a Poisson point process of intensity λ on a bounded region in d-space, and ξx is a functional determined by the Poisson points near to x, i.e. satisfying an exponential stabilization condition, along with a moments condition (examples include statistics for proximity graphs, germ-grain models and random sequential deposition models). A known general resu...

Screening for a Multivariate Mixture Normal Distribution

A novel series expansion for the multivariate normal probability integrals based on Fourier series

Abstract. In this article, we derive a series expansion of the multivariate normal probability integrals based on Fourier series. The basic idea is to transform the limits of each integral from hi to ∞ to be from −∞ to ∞ by multiplying the integrand by a periodic square wave that approximates the domain of the integral. This square wave is expressed by its Fourier series expansion. Then a Chole...

On crossing minimization problem

In this paper we consider a problem related to global routing post-optimization: the crossing minimization problem (CMP). Given a global routing representation, the CMP is to minimize redundant crossings between every pair of nets. In particular, there are two kinds of CMP: constrained CMP (CCMP) and unconstrained CMP (UCMP). These problems have been studied previously in Groe89], where an O(m ...

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.