Limit Theorems for Some Long Range Random Walks on Torsion Free Nilpotent Groups

Zhen-Qing Chen is a Professor of Mathematics at the University of Washington, Seattle, Washington, USATakashi Kumagai is a Professor of Mathematics  at Waseda University, Tokyo, Japan.Laurent Saloff-Coste is the Abram R. Bullis Professor of Mathematics at Cornell University, Ithaca, New York, USA.Jian Wang is a Professor of Mathematics at Fujian Normal University, Fuzhou, Fujian Province, P.R. ChinaTianyi Zheng is a Professor of Mathematics at the University of California, San Diego, California, USA

• 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).