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Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups
◆Springer Yellow セール開催中！：2025年6月29日(日)ご注文分まで
※上記表示の販売価格は割引適用後の価格です 出版済み 3週間でお届けいたします。 Series: SpringerBriefs in Mathematics Author: Chen, Zhen-Qing/ Kumagai, Takashi/ Saloff-Coste, Laurent/ Wang, Jian/ Zheng, Tianyi Publisher: Springer ISBN: 9783031433313 Cover: PAPERBACK Date: 2023年10月 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 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. TABLE OF 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 Levy 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).
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