University of Newcastle upon Tyne

School of Mathematics and Statistics

Statistics Seminars 2004-2005

28 January 2005, L401, 2:15pm

Professor John Biggins, University of Sheffield

Abstract

Suppose p(x) is a probability generating function which is a polynomial of degree ρ; denote the nth iterate of the polynomial by pⁿ. When pⁿ(x) goes to infinity with n, it is not to hard to show that ρ^-nlog pⁿ(x) converges to a finite strictly positive limit and to establish various properties of this limit. This has been known for a very long time.

The analogous problem for multivariate generating functions of finite degree, which will be the main focus for the talk, is harder because there is no simple direct counterpart to the highest power. The initial stimulus for thinking about this was results of Miller and O'Sullivan (1992) on enumeration issues in `context free languages'; their results can be improved using the theory developed.

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