Branching Processes Learning Seminar

Sascha Troscheit, Department of Pure Mathematics, University of Waterloo

"Branching Processes, Martingales, Kingman’s Subadditive Ergodic Theorem, and some applications, Part IV: Kingman’s Subadditive Ergodic Theorem"

And now for something completely different. We leave Galton-Watson processes behind and talk a bit about Birkhoff’s Ergodic Theorem and Fekete’s Lemma. The latter states that a_n/n converges if a_n is a subadditive sequence and Kingman’s subadditive ergodic theorem provides a dynamical / random analogue.

We will provide a short(-ish) proof of the subadditive ergodic theorem due to Steele and provide some simple applications to prepare us for some exciting(?) modern branching processes in Part V.

MC 5417