02966nam 22005895 450 991075508320332120231024230547.03-031-43332-710.1007/978-3-031-43332-0(MiAaPQ)EBC30825284(Au-PeEL)EBL30825284(DE-He213)978-3-031-43332-0(PPN)27291570X(EXLCZ)992855169960004120231024d2023 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierLimit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups[electronic resource] /by Zhen-Qing Chen, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, Tianyi Zheng1st ed. 2023.Cham :Springer Nature Switzerland :Imprint: Springer,2023.1 online resource (147 pages)SpringerBriefs in Mathematics,2191-8201Print version: Chen, Zhen-Qing Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups Cham : Springer,c2023 9783031433313 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.SpringerBriefs in Mathematics,2191-8201ProbabilitiesMathematicsProbability TheoryApplied ProbabilityMathematicsProbabilities.Mathematics.Probability Theory.Applied Probability.Mathematics.519.2Chen Zhen-Qing514801Kumagai Takashi525017Saloff-Coste Laurent60712Wang Jian525063Zheng Tianyi1435999MiAaPQMiAaPQMiAaPQBOOK9910755083203321Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups3594030UNINA