Dimension Spectrum for a Nonconventional Ergodic Average

Yuval Peres; Boris Solomyak

Dimension Spectrum for a Nonconventional Ergodic Average

Yuval Peres ,
Boris Solomyak

Real Analysis Exchange | July 2011 , Vol 37: pp. 375-388

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We compute the dimension spectrum of certain nonconventional averages, namely, the Hausdorff dimension of the set of 0,1 sequences, for which the frequency of the pattern 11 in positions k,2kequals a given number θ∈[0,1].