Geodesic
Spectral statistics for random Schrödinger operators in the localized regime
Journal of the European Mathematical Society, Tome 16 (2014) no. 9, pp. 1967-2031 Cet article a éte moissonné depuis la source EMS Press

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We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy E in the localized phase. Assume the density of states function is not too flat near E. Restrict it to some large cube . Consider now I, a small energy interval centered at E that asymptotically contains infintely many eigenvalues when the volume of the cube grows to infinity. We prove that, with probability one in the large volume limit, the eigenvalues of the random Hamiltonian restricted to the cube inside the interval are given by independent identically distributed random variables, up to an error of size an arbitrary power of the volume of the cube. As a consequence, we derive
DOI : 10.4171/jems/481
Classification : 81-XX, 60-XX
Keywords: Random Schrödinger operators, eigenvalue statistics, level spacing distribution 
@article{JEMS_2014_16_9_a6,
     author = {Fran\c{c}ois Germinet and Fr\'ed\'eric Klopp},
     title = {Spectral statistics for random {Schr\"odinger} operators in the localized regime},
     journal = {Journal of the European Mathematical Society},
     pages = {1967--2031},
     year = {2014},
     volume = {16},
     number = {9},
     doi = {10.4171/jems/481},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/481/}
}
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François Germinet; Frédéric Klopp. Spectral statistics for random Schrödinger operators in the localized regime. Journal of the European Mathematical Society, Tome 16 (2014) no. 9, pp. 1967-2031. doi: 10.4171/jems/481

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