Titlebook: Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups; Zhen-Qing Chen,Takashi Kumagai,Tianyi Zheng Book 2023 Th

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Measures in , and Their Geometries,sures on .. For each measure . in ., a particular “geometry” associated with . is defined. This geometry will later be the key needed to understand how to define norms and appropriate approximate dilations adapted to the measure . in order to apply the limit theorems of Chaps. . and ..

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Zhen-Qing Chen,Takashi Kumagai,Tianyi ZhengProvides a systematic study of functional limit theorem for long-jump random walks on nilpotent groups.Gives a companion local limit theorem relating the densities of‘of the associated processes.Prese

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Book 2023hese 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 invol

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,Symmetric Lévy Processes on Nilpotent Groups,one hand and the limit theorems obtained in Chaps. . and . on the other hand. Several examples are given to illustrate the limit theorems explicitly using this approach. Examples discussed in Chap. . are also revisited in this new light.

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2191-8198 fers 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..978-3-031-43331-3978-3-031-43332-0Series ISSN 2191-8198 Series E-ISSN 2191-8201

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Weak Convergence of the Processes,the present setting. These conditions are not only phrased mostly in terms of the given random walk but also involve the existence of an appropriate approximate dilation. All together, they are rather strong conditions and finding ways to work under less stringent hypotheses is an interesting open problem.