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 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...
متن کاملEntropy and Ergodic Theory
Modern information theory was born in Shannon’s 1948 paper “A Mathematical Theory of Communication” [Sha48]. The mathematical expression for entropy is older, originating in statistical physics. But it was Shannon’s work that instigated the study of its purely mathematical properties, and uncovered the importance of the type-multiplicity and related problems. For simplicity, let us consider an ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1968
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1968-0224770-7