Applebaum D. Probability on Compact Lie Groups

Springer International Publishing, Switzerland, 2014. — 217 p.Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications.Lie groups.
Representations, Peter–Weyl theory and weights.
Analysis on compact Lie groups.
Probability measures on compact Lie groups.
Convolution semigroups of measures.
Deconvolution density estimation.