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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The Main Results for Random Walks Driven by Measures in ,ability measures in .. This chapter is devoted to verifying that such probability measures satisfy the properties set forth in Chaps. . and ., properties that were proved in those chapters to be sufficient to obtain both a functional limit theorem (Theorem .) and a local limit theorem (Theorem .). T

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978-3-031-43331-3The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Polynomial Coordinates and Approximate Dilations,a suitable dilation structures is key to the formulation of limit theorems for random walks on groups. One of the main tools used in this book is the notion of approximate group dilations. The limit group structures that appear when one uses rescaling associated with approximate group dilations are discussed.

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Vague Convergence and Change of Group Law,ated with the driving probability measure of a long-range random walk to the vague convergence of the associated jump kernels. This involves taking into account the change of group law induced by the rescaling of space through an approximate group dilation.

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