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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. 

We report a diastereoconvergent synthesis of anti -1,2-amino alcohols bearing N-containing quaternary stereocenters using an intermolecular direct C–H amination of homoallylic alcohol derivatives catalyzed by a phosphine selenide. Destruction of the allylic stereocenter during the selenium-catalyzed process allows selective formation of a single diastereomer of the product starting from any diastereomeric mixture of the starting homoallylic alcohol derivatives, eliminating the need for the often-challenging diastereoselective preparation of starting materials. Mechanistic studies show that the diastereoselectivity is controlled by a stereoelectronic effect (inside alkoxy effect) on the transition state of the final [2,3]-sigmatropic rearrangement, leading to the observed anti selectivity. The power of this protocol is further demonstrated on an extension to the synthesis of syn -1,4-amino alcohols from allylic alcohol derivatives, constituting a rare example of 1,4-stereoinduction.