Abstract

A new version of the Frohlich -- Spencer coupling lemma T. Kriecherbauer We consider matrices with entries decaying rapidly away from the diagonal. We present a new technique how to construct the inverse matrix from a sufficiently large collection of local inverses (i.e. inverses of submatrices). Such a coupling lemma was first introduced in 1983 by Fr\"ohlich and Spencer in order to prove localisation for the Anderson model via a multiscale analysis. Subsequently, the coupling lemma proved to be a useful tool in the study of discrete Schr\"odinger operators with random or quasi-periodic potentials.

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