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The purpose of the present work is to establish decorrelation estimates atdistinct energies for some random Schr{\"o}dinger operator in dimension one. Inparticular, we establish the result for some random operators on the continuumwith alloy-type potential without covering condition assumption. These resultsare used to give a description of the spectral statistics.

Decorrelation estimates for some continuous and discrete random Schr{\"o}dinger operators in dimension one, without covering condition