Ergodic Theorems for Group Actions: Informational and Thermodynamical Aspects (Mathematics and Its Applications, 78)
ISBN-13:
9789048141555
ISBN-10:
9048141559
Edition:
Softcover reprint of the original 1st ed. 1992
Author:
A.A. Tempelman
Publication date:
2010
Publisher:
Springer
Format:
Paperback
417 pages
FREE US shipping
Book details
ISBN-13:
9789048141555
ISBN-10:
9048141559
Edition:
Softcover reprint of the original 1st ed. 1992
Author:
A.A. Tempelman
Publication date:
2010
Publisher:
Springer
Format:
Paperback
417 pages
Summary
Ergodic Theorems for Group Actions: Informational and Thermodynamical Aspects (Mathematics and Its Applications, 78) (ISBN-13: 9789048141555 and ISBN-10: 9048141559), written by authors
A.A. Tempelman, was published by Springer in 2010.
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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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