  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.
