Spacings and pair correlations for finite Bernoulli convolutions

Itai Benjamini, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We consider finite Bernoulli convolutions with a parameter 1/2 < λ < 1 supported on a discrete point set, generically of size 2 N. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure νλ, as N → ∞. Numerical evidence suggests that for a generic λ, the distribution of spacings between appropriately rescaled points is Poissonian. We obtain some partial results in this direction; for instance, we show that, on average, the pair correlations do not exhibit attraction or repulsion in the limit. On the other hand, for certain algebraic λ the behaviour is totally different.

Original languageEnglish
Pages (from-to)381-393
Number of pages13
JournalNonlinearity
Volume22
Issue number2
DOIs
StatePublished - 2009
Externally publishedYes

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