Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups (Springerbriefs in Mathematics)

Chen, Zhen-Qing/ Kumagai, Takashi/ Saloff-Coste, Laurent

Springer International Publishing AG（2023/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 139 p.
• 商品コード 9783031433313

Full Description

This book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups.  The limits in these limit theorems are Lévy processes on some simply connected nilpotent Lie groups. Both the limit Lévy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk. The book offers the first systematic study of such limit theorems involving stable-like random walks and stable limit Lévy processes in the context of (non-commutative) nilpotent groups.

Contents

Setting the stage.- Introduction.- Polynomial coordinates and approximate dilations.- Vague convergence and change of group law.- Weak convergence of the processes.- Local limit theorem.- Symmetric Lévy processes on nilpotent groups.- Measures in SM(Γ) and their geometries.- Adapted approximate group dilations.- The main results for random walks driven by measures in SM(Γ).