Displaying similar documents to “Correlation asymptotics from large deviations in dynamical systems with infinite measure”

On the correlation of families of pseudorandom sequences of k symbols

Kit-Ho Mak, Alexandru Zaharescu (2016)

Acta Arithmetica

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In an earlier paper Gyarmati introduced the notion of f-correlation for families of binary pseudorandom sequences as a measure of randomness in the family. In this paper we generalize the f-correlation to families of pseudorandom sequences of k symbols and study its properties.

Fubini’s Theorem on Measure

Noboru Endou (2017)

Formalized Mathematics

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The purpose of this article is to show Fubini’s theorem on measure [16], [4], [7], [15], [18]. Some theorems have the possibility of slight generalization, but we have priority to avoid the complexity of the description. First of all, for the product measure constructed in [14], we show some theorems. Then we introduce the section which plays an important role in Fubini’s theorem, and prove the relevant proposition. Finally we show Fubini’s theorem on measure.

Poisson suspensions of compactly regenerative transformations

Roland Zweimüller (2008)

Colloquium Mathematicae

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For infinite measure preserving transformations with a compact regeneration property we establish a central limit theorem for visits to good sets of finite measure by points from Poissonian ensembles. This extends classical results about (noninteracting) infinite particle systems driven by Markov chains to the realm of systems driven by weakly dependent processes generated by certain measure preserving transformations.

A Note on the Measure of Solvability

D. Caponetti, G. Trombetta (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let X be an infinite-dimensional Banach space. The measure of solvability ν(I) of the identity operator I is equal to 1.

Construction of Measure from Semialgebra of Sets1

Noboru Endou (2015)

Formalized Mathematics

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In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore,...

On a paper by Castelli, Mignosi, Restivo

Jacques Justin (2010)

RAIRO - Theoretical Informatics and Applications

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Fine and Wilf's theorem has recently been extended to words having three periods. Following the method of the authors we extend it to an arbitrary number of periods and deduce from that a characterization of generalized Arnoux-Rauzy sequences or episturmian infinite words.

Product Pre-Measure

Noboru Endou (2016)

Formalized Mathematics

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In this article we formalize in Mizar [5] product pre-measure on product sets of measurable sets. Although there are some approaches to construct product measure [22], [6], [9], [21], [25], we start it from σ-measure because existence of σ-measure on any semialgebras has been proved in [15]. In this approach, we use some theorems for integrals.

Waiting for long excursions and close visits to neutral fixed points of null-recurrent ergodic maps

Roland Zweimüller (2008)

Fundamenta Mathematicae

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We determine, for certain ergodic infinite measure preserving transformations T, the asymptotic behaviour of the distribution of the waiting time for an excursion (from some fixed reference set of finite measure) of length larger than l as l → ∞, generalizing a renewal-theoretic result of Lamperti. This abstract distributional limit theorem applies to certain weakly expanding interval maps, where it clarifies the distributional behaviour of hitting times of shrinking neighbourhoods of...

Algebra of Polynomially Bounded Sequences and Negligible Functions

Hiroyuki Okazaki (2015)

Formalized Mathematics

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In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation...

On v-positive type transformations in infinite measure

Tudor Pădurariu, Cesar E. Silva, Evangelie Zachos (2015)

Colloquium Mathematicae

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For each vector v we define the notion of a v-positive type for infinite-measure-preserving transformations, a refinement of positive type as introduced by Hajian and Kakutani. We prove that a positive type transformation need not be (1,2)-positive type. We study this notion in the context of Markov shifts and multiple recurrence, and give several examples.

Measure of non-compactness of operators interpolated by the real method

Radosław Szwedek (2006)

Studia Mathematica

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We study the measure of non-compactness of operators between abstract real interpolation spaces. We prove an estimate of this measure, depending on the fundamental function of the space. An application to the spectral theory of linear operators is presented.

Completely mixing maps without limit measure

Gerhard Keller (2004)

Colloquium Mathematicae

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We combine some results from the literature to give examples of completely mixing interval maps without limit measure.