We present new scale-free quantitative unique continuation principles for Schrodinger operators. They apply to linear combinations of eigenfunctions corresponding to eigenvalues below a prescribed energy, and can be formulated as an uncertainty principle for spectral projectors. This extends recent results of Rojas-Molina & Veselic [15], and Klein [10]. We apply the scale-free unique continuation principle to obtain a Wegner estimate for a random Schrodinger operator of breather type. It holds for arbitrarily high energies. Schrodinger operators with random breather potentials have a non-linear dependence on random variables. We explain the challenges arising from this non-linear dependence. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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