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Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups
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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 Lvy processes on some simply connected nilpotent Lie groups. Both the limit Lvy 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 Lvy processes in the context of (non-commutative) nilpotent groups.
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