On the Asymptotic Variance of Vacancy for Boolean Models with Grain Distortions

Host Institution:

LaTrobe University

Title of Seminar:

On the Asymptotic Variance of Vacancy for Boolean Models with Grain Distortions

Speaker's Name:

Christian Rau

Speaker's Institution:

Monash University

Time and Date:

11am Friday 14 November 2008

Seminar Abstract:

A Boolean model is a spatial coverage process whose driving point process is homogeneous Poisson, and whose attached random sets, or grains, are independent and identically distributed (i.i.d). Apart from a host of traditional applications, Boolean models have been employed recently in the modelling of sensor networks, which motivated this research. The asymptotic variance of vacancy (AVV) in the Boolean model is defined by letting the intensity of the Poisson process diverge to infinity, and simultaneously scaling the grains to become small. We consider optimality and continuity properties of the AVV when the grains are subject to i.i.d. distortions, which includes rotations and shearings as special cases. An important role in the formulation and derivation of our results is played by notions of symmetry well known from multivariate analysis and stochastic simulation, such as conjugation-invariance and group models.

This is joint work with Sung Nok Chiu, Hong Kong Baptist University.


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