che-chandler.de
|
| Der Artikel wird am Ende des Bestellprozesses zum Download zur Verfügung gestellt. |
Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups
ISBN-13:
9783031433320
Veröffentl:
2023
Einband:
eBook
Seiten:
139
Autor:
Zhen-Qing Chen
Serie:
SpringerBriefs in Mathematics
eBook Typ:
PDF
eBook Format:
Reflowable eBook
Kopierschutz:
Digital Watermark [Social-DRM]
Sprache:
Englisch
Beschreibung:
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 Levy processes on some simply connected nilpotent Lie groups. Both the limit Levy 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 Levy processes in the context of (non-commutative) nilpotent groups.
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.
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).