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. © Institute of Mathematical Statistics, 2009.
Matching with shift for one-dimensional Gibbs measures / Giardina', Cristian; P., Collet; F., Redig. - In: THE ANNALS OF APPLIED PROBABILITY. - ISSN 1050-5164. - STAMPA. - 19:(2009), pp. 1581-1602. [10.1214/08-AAP588]
Matching with shift for one-dimensional Gibbs measures
GIARDINA', Cristian;
2009
Abstract
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. © Institute of Mathematical Statistics, 2009.
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