Charles Kenney, Rutgers University

Abstract

A Poisson random variable Y with parameter t has, for all n in N, probability(Y=n) = t^n / (n! e^t). The Brun sieve is a method in the Poisson Paradigm/Poisson approximation, a rich and deep area of probability theory in which random variables that can be expressed as sums of indicators of rare, mostly-independent events, are shown to be almost Poisson. In this talk I will prove the basic Brun sieve theorem and show its application to combinatorics and (time permitting) number theory.