منابع مشابه
Ergodic theorem, ergodic theory, and statistical mechanics.
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...
متن کاملErgodic Properties of Boundary Actions and Nielsen–schreier Theory
We study the basic ergodic properties (ergodicity and conservativity) of the action of a subgroup H of a free group F on the boundary ∂F with respect to the uniform measure. Our approach is geometrical and combinatorial, and it is based on choosing a system of Nielsen–Schreier generators in H associated with a geodesic spanning tree in the Schreier graph X = H\F . We give several (mod 0) equiva...
متن کاملErgodic Theory and Number Theory
Elon Lindenstrauss was awarded the 2010 Fields Medal for his results on measure rigidity in ergodic theory, and their applications to number theory. The web page of the ICM 2010 contains the following brief description of Elon Lindenstrauss’ achievements: Lindenstrauss has made far-reaching advances in ergodic theory, the study of measure preserving transformations. His work on a conjecture of ...
متن کاملErgodic Theory
Ergodic theory involves the study of transformations on measure spaces. Interchanging the words “measurable function” and “probability density function” translates many results from real analysis to results in probability theory. Ergodic theory is no exception. Ergodic theory has fundamental applications in probability theory, starting from areas that are very well understood, such as finite st...
متن کاملAnalysis and Ergodic Theory
We cover the second half of Green and Tao’s proof of the existence of arbitrarily long arithmetic progressions of prime numbers, by constructing a function and pseudorandom measure suitably associated to the primes. 1.1 Orienting remarks The proof of the Green-Tao Theorem breaks conveniently into two distinct stages: 1. First, it is shown how the conclusion of Szemerédi’s Theorem can be extende...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1976
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.73.6.1802