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Pré-Publication, Document De Travail Année : 2023

Phase transition in the Integrated Density of States of the Anderson model arising from a supersymmetric sigma model

Résumé

We study the Integrated Density of States (IDS) of the random Schr\"odinger operator appearing in the study of certain reinforced random processes in connection with a supersymmetric sigma-model. We rely on previous results on the supersymmetric sigma-model to obtain lower and upper bounds on the asymptotic behavior of the IDS near the bottom of the spectrum in all dimension. We show a phase transition for the IDS between weak and strong disorder regime in dimension larger or equal to three, that follows from a phase transition in the corresponding random process and supersymmetric sigma-model. In particular, we show that the IDS does not exhibit Lifshitz tails in the strong disorder regime, confirming a recent conjecture. This is in stark contrast with other disordered systems, like the Anderson model. A Wegner type estimate is also derived, giving an upper bound on the IDS and showing the regularity of the function.

Dates et versions

hal-04335215 , version 1 (11-12-2023)

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Margherita Disertori, Valentin Rapenne, Constanza Rojas-Molina, Xiaolin Zeng. Phase transition in the Integrated Density of States of the Anderson model arising from a supersymmetric sigma model. 2023. ⟨hal-04335215⟩
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