variation in probability, ergodic theory and analysis
نویسندگان
چکیده
منابع مشابه
Ergodic Theory and Connections with Analysis and Probability
In this paper we establish a variety or results in ergodic theory by using techniques from probability and analysis. We discuss divergence of operators, including strong sweeping out and Bourgain’s entropy method. We consider square functions, oscillation operators, and variational operators for ergodic averages. We also consider almost everywhere convergence of convolution powers.
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15 صفحه اولAnalysis 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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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 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 ...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1998
ISSN: 0019-2082
DOI: 10.1215/ijm/1255985619