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＜E-Book＞
Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups / by Zhen-Qing Chen, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, Tianyi Zheng
(SpringerBriefs in Mathematics. ISSN:21918201)

Edition	1st ed. 2023.
Publisher	(Cham : Springer Nature Switzerland : Imprint: Springer)
Year	2023
Language	English
Size	XIII, 139 p : online resource
Authors	*Chen, Zhen-Qing author Kumagai, Takashi author Saloff-Coste, Laurent author Wang, Jian author Zheng, Tianyi author SpringerLink (Online service)
Subjects	LCSH:Probabilities LCSH:Mathematics FREE:Probability Theory FREE:Applied Probability FREE:Mathematics
Notes	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) 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 HTTP:URL=https://doi.org/10.1007/978-3-031-43332-0

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