Ergodic Theorems for Group Actions
Subtitle: Informational and Thermodynamical Aspects
By: by Arkady Tempelman
Series: Mathematics and Its Applications -- 78; Mathematics and Its Applications -- 78
Publisher: Springer Netherlands
Published: 1992
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 399
ISBN-13: 9789048141555; 9789401714600
Subjects: Harmonic analysis; Functional analysis; Statistics; Mathematics
Description: This volume is devoted to generalizations of the classical Birkhoff and von Neuman ergodic theorems to semigroup representations in Banach spaces, semigroup actions in measure spaces, homogeneous random fields and random measures on homogeneous spaces. The ergodicity, mixing and quasimixing of semigroup actions and homogeneous random fields are considered as well. In particular homogeneous spaces, on which all homogeneous random fields are quasimixing are introduced and studied (the n-dimensional Euclidean and Lobachevsky spaces with n>=2, and all simple Lie groups with finite centre are examples of such spaces. Also dealt with are applications of general ergodic theorems for the construction of specific informational and thermodynamical characteristics of homogeneous random fields on amenable groups and for proving general versions of the McMillan, Breiman and Lee-Yang theorems. A variational principle which characterizes the Gibbsian homogeneous random fields in terms of the specific free energy is also proved. The book has eight chapters, a number of appendices and a substantial list of references. For researchers whose works involves probability theory, ergodic theory, harmonic analysis, measure theory and statistical Physics.
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