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Probability on Algebraic Structures
Edited by: Gregory Budzban and Philip Feinsilver, Southern Illinois University, Carbondale, IL, and Arunava Mukherjea, University of South Florida, Tampa, FL
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Contemporary Mathematics
2000; 238 pp; softcover
Volume: 261
ISBN-10: 0-8218-2027-3
ISBN-13: 978-0-8218-2027-8
List Price: US$68 Member Price: US$54.40
Order Code: CONM/261

This volume presents results from an AMS Special Session held on the topic in Gainesville (FL). Papers included are written by an international group of well-known specialists who offer an important cross-section of current work in the field. In addition there are two expository papers that provide an avenue for non-specialists to comprehend problems in this area.

The breadth of research in this area is evident by the variety of articles presented in the volume. Results concern probability on Lie groups and general locally compact groups. Generalizations of groups appear as hypergroups, abstract semigroups, and semigroups of matrices. Work on symmetric cones is included. Lastly, there are a number of articles on the current progress in constructing stochastic processes on quantum groups.

Graduate students and research mathematicians interested in probability, topology, functional analysis, and group theory.

Lie groups, topological groups
• S. G. Dani and R. Shah -- Contractible measures in Levy's measures on Lie groups
• P. Feinsilver and R. Schott -- Lie response to signals with noise
• W. Jaworski -- On shifted convolution powers and concentration functions in locally compact groups
• M. McCrudden and S. Walker -- Embedding infinitely divisible probabilities on subsemigroups of Lie groups
• D. Neuenschwander -- s-stable semigroups on simply connected step 2-nilpotent Lie groups
Hypergroups
• H. Heyer -- The covariance distribution of a generalized random field over a commutative hypergroup
• C. Rentzsch and M. Voit -- Lévy processes on commutative hypergroups
Symmetric cones, Wishart distributions
• G. Letac -- Symmetric cones as Gelfand pairs: Probabilistic applications
• G. Letac and H. Massam -- Representations of the Wishart distributions
Quantum groups, quantum probability
• L. Accardi -- Quantum probability: An historical survey
• U. Franz -- Lévy processes on quantum groups
• V. K. Dobrev, H.-D. Doebner, U. Franz, and R. Schott -- Lévy processes on $$U_q(\mathfrak{g})$$ as infinitely divisible representations
Semigroups, matrices, applications
• G. Budzban and A. Mukherjea -- A semigroup approach to the road coloring problem
• G. Högnäs -- On some one-dimensional stochastic population models
• Z. J. Jurek -- Three algebraic problems in probability theory
• A. Mukherjea -- Products of i.i.d. $$d \times d$$ real matrices: Convergence in direction