Probabilities on the Heisenberg Group

1. Front Matter

   Pages i-viii

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2. Introduction

   • Daniel Neuenschwander

   Pages 1-6

3. Probability theory on simply connected nilpotent Lie groups

   • Daniel Neuenschwander

   Pages 7-27

4. Brownian motions on H

   • Daniel Neuenschwander

   Pages 29-84

5. Other limit theorems on H

   • Daniel Neuenschwander

   Pages 85-123

6. Back Matter

   Pages 125-139

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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.

• Brownian motion
• Probability theory
• functional analysis
• linear optimization
• mechanics
• operator
• quantum mechanics

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