Felipe Hernández

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math-ph2025

Self-consistent equations and quantum diffusion for the Anderson model

Adam Black, Reuben Drogin, Felipe Hernández

We consider the Anderson tight-binding model on $Z^{d}$ , $d \geq 2$ , with Gaussian noise and at low disorder $λ > 0$ . We derive a diffusive scaling limit for the entries of the…

math-ph2025

Tail bounds for the Dyson series of random Schrödinger equations

Adam Black, Reuben Drogin, Felipe Hernández

We study Schrödinger equations on $Z^{d}$ and $R^{d}$ , $d \geq 2$ with random potentials of strength $λ$ . Our main result gives tail bounds for the terms of the Dyson…