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
CONTENT
Probability theory on simply connected nilpotent Lie groups -- Brownian motions on H -- Other limit theorems on H
Mathematics
Topological groups
Lie groups
Probabilities
Physics
Computational intelligence
Mathematics
Probability Theory and Stochastic Processes
Topological Groups Lie Groups
Theoretical Mathematical and Computational Physics
