The present volume contains the transactions of the lOth Oberwolfach Conference on "Probability Measures on Groups". The series of these meetings inaugurated in 1970 by L. Schmetterer and the editor is devoted to an intensive exchange of ideas on a subject which developed from the relations between various topics of mathematics: measure theory, probability theory, group theory, harmonic analysis, special functions, partial differential operators, quantum stochastics, just to name the most significant ones. Over the years the fruitful interplay broadened in various directions: new group-related structures such as convolution algebras, generalized translation spaces, hypercomplex systems, and hypergroups arose from generalizations as well as from applications, and a gradual refinement of the combinatorial, Banach-algebraic and Fourier analytic methods led to more precise insights into the theory. In a period of highest specialization in scientific thought the separated minds should be reunited by actively emphasizing similarities, analogies and coincidences between ideas in their fields of research. Although there is no real separation between one field and another - David Hilbert denied even the existence of any difference between pure and applied mathematics - bridges between probability theory on one side and algebra, topology and geometry on the other side remain absolutely necessary. They provide a favorable ground for the communication between apparently disjoint research groups and motivate the framework of what is nowadays called "Structural probability theory".
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ISBN-13
978-1-4899-2364-6 (9781489923646)
DOI
10.1007/978-1-4899-2364-6
Schweitzer Klassifikation
Homoclinic points Cr-created under hypotheses by probability measures.- An approximate martingale convergence theorem on locally compact abelian groups.- Positive definite functions and the Lévy continuity theorem for commutative hypergroups.- A Hunt-Stein theorem for amenable semigroups.- Jacobi polynomials and related hypergroup structures.- Discrete time voter models: a class of stochastic automata.- Theoretical and distributional aspects of shape analysis.- Speed of convergence of transformed convolution powers of a probability measure on a compact connected group.- Krawtchouk polynomials and finite probability theory.- On some multidimensional integral transforms and their connection with the theory of hypergroups.- The transience criterion for semigroups of probability measures on a class of commutative hypergroups.- Applications of symmetry groups in Markov processes.- Classes of trimeasures: Applications of harmonic analysis.- A study of some stationary Gaussian processes indexed by the homogeneous tree.- Semistability and domains of attraction on compact extensions of nilpotent groups.- Poisson boundaries of random walks on discrete solvable groups.- The domain of normal attraction of a stable probability measure on a nilpotent group.- Positive convolution structures associated with quantum groups.- Regularity and singularity of weakly stationary processes indexed by a commutative hypergroup.- Construction of quasi invariant probability measures on some current groups of continuous sections of a bundle of compact semisimple Lie groups.- An example of a solvable Lie group admitting an absolutely continuous Gauss semigroup with incomparable supports.- Invariant probability measures on compact right topological groups.- Semigroups, attractors, and products ofrandom matrices.- Isometric operators on L1-algebras of hypergroups.- A new proof of the central limit theorem on stratified Lie groups.- Semigroups in probability theory.- Infinite convolution of distributions on discrete commutative semigroups.- Realization of unitary q-white noise on Fock space.- Bernstein polynomials and random walks on hypergroups.- Permutation operators and the central limit theorem associated with partial differential operators.- A generalization of orbital morphisms of hypergroups.- A complete invariant of a locally compact group.- Behaviour at infinity and harmonic functions of random walks on graphs.- Counterexamples in algebraic probability theory.- Duality of commutative hypergroups.- Participants.
