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200 10$aLimit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups$b[electronic resource] /$fby Zhen-Qing Chen, Takashi Kumagai, Laurent Saloff-Coste, Jian Wang, Tianyi Zheng
205   $a1st ed. 2023.
210  1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023.
215   $a1 online resource (147 pages)
225 1 $aSpringerBriefs in Mathematics,$x2191-8201
311 08$aPrint version: Chen, Zhen-Qing Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups Cham : Springer,c2023 9783031433313 
327   $aSetting 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(?) and their geometries -- Adapted approximate group dilations -- The main results for random walks driven by measures in SM(?).
330   $aThis book develops limit theorems for a natural class of long range random walks on finitely generated torsion free nilpotent groups. The limits in these limit theorems are Lévy processes on some simply connected nilpotent Lie groups. Both the limit Lévy process and the limit Lie group carrying this process are determined by and depend on the law of the original random walk. The book offers the first systematic study of such limit theorems involving stable-like random walks and stable limit Lévy processes in the context of (non-commutative) nilpotent groups.
410  0$aSpringerBriefs in Mathematics,$x2191-8201
606   $aProbabilities
606   $aMathematics
606   $aProbability Theory
606   $aApplied Probability
606   $aMathematics
615  0$aProbabilities.
615  0$aMathematics.
615 14$aProbability Theory.
615 24$aApplied Probability.
615 24$aMathematics.
676   $a519.2
700   $aChen$b Zhen-Qing$0514801
701   $aKumagai$b Takashi$0525017
701   $aSaloff-Coste$b Laurent$060712
701   $aWang$b Jian$0525063
701   $aZheng$b Tianyi$01435999
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910755083203321
996   $aLimit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups$93594030
997   $aUNINA