Matching with shift for one-dimensional Gibbs measures

Details Matching with shift for one-dimensional Gibbs measures Matching with shift for one-dimensional Gibbs measures

2007-08-16

arxiv.org/abs/0708.2165v3

Annals of Applied Probability 2009, Vol. 19, No. 4, 1581-1602

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP588 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP588

We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in terms of the thermodynamic quantities (pressure) of the underlying potential. Our approach is based on the analysis of the first and second moment of the number of overlaps of a given size. We treat both the case of equal sequences (and nonzero shifts) and independent sequences.

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