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Limit theorems for some long range random walks on torsion free nilpotent groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	Limit theorems for some long range random walks on torsion free nilpotent groupsby Zhen-Qing Chen ... [et al.].
other author:	Chen, Zhen-Qing.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	xiii, 139 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Limit theorems (Probability theory)
Online resource:	https://doi.org/10.1007/978-3-031-43332-0
ISBN:	9783031433320$q(electronic bk.)

Limit theorems for some long range random walks on torsion free nilpotent groups
Limit theorems for some long range random walks on torsion free nilpotent groups[electronic resource] /by Zhen-Qing Chen ... [et al.]. - Cham :Springer Nature Switzerland :2023. - xiii, 139 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

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.

ISBN: 9783031433320$q(electronic bk.)

Standard No.: 10.1007/978-3-031-43332-0doiSubjects--Topical Terms:

182695
Limit theorems (Probability theory)

LC Class. No.: QA273.67

Dewey Class. No.: 519.2

Limit theorems for some long range random walks on torsion free nilpotent groups
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505 0 $a 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)
520 $a 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.
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