Probabilities on the Heisenberg group : limit theorems and Brownian motion

Bibliographic Information

Probabilities on the Heisenberg group : limit theorems and Brownian motion

Daniel Neuenschwander

(Lecture notes in mathematics, 1630)

Springer, c1996

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Note

Includes bibliography (p. 125-136) and index

Description and Table of Contents

Description

The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.

Table of Contents

Probability theory on simply connected nilpotent Lie groups.- Brownian motions on H.- Other limit theorems on H.

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