Matching with shift for one-dimensional Gibbs measures
Probability
2009-09-01 v3 Mathematical Physics
math.MP
Abstract
We consider matching with shifts for Gibbsian sequences. We prove that the maximal overlap behaves as , where 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.
Keywords
Cite
@article{arxiv.0708.2165,
title = {Matching with shift for one-dimensional Gibbs measures},
author = {P. Collet and C. Giardina and F. Redig},
journal= {arXiv preprint arXiv:0708.2165},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AAP588 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)