Branching Random Walks : École d'Été de Probabilités de Saint-Flour XLII - 2012 (École d'Été de Probabilités de Saint-flour)

Shi, Zhan

Springer International Publishing AG（2016/02発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 133 p.
• 商品コード 9783319253718

Full Description

Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time.

Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees.

Contents

I Introduction.- II Galton-Watson trees.- III Branching random walks and martingales.- IV The spinal decomposition theorem.- V Applications of the spinal decomposition theorem.- VI Branching random walks with selection.- VII Biased random walks on Galton-Watson trees.- A Sums of i.i.d. random variables.- References.