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This book addresses the direct imaging of hydrogen-bond dynamics within water-based model systems assembled on a metal surface, using a scanning tunneling microscope (STM).

The hydrogen bond represents an important interaction between molecules, and the dynamics of hydrogen bonds in water create an ever-present question associated with the process of chemical and biological reactions. In spite of numerous studies, the process remains poorly understood at the microscopic level because hydrogen-bond dynamics, such as bond rearrangements and hydrogen/proton transfer reactions, are extremely difficult to probe. Those studies have been carried out by means of spectroscopic methods where the signal stems from the ensemble of a system and the hydrogen-bond dynamics...

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.