Integrated density of states of the Anderson Hamiltonian with two-dimensional white noise

Toyomu Matsuda

Stochastic Processes and their Applications, 2022, vol. 153, issue C, 91-127

Abstract: We construct the integrated density of states of the Anderson Hamiltonian with two-dimensional white noise by proving the convergence of the Dirichlet eigenvalue counting measures associated with the Anderson Hamiltonians on the boxes. We also determine the logarithmic asymptotics of the left tail of the integrated density of states. Furthermore, we apply our result to a moment explosion of the parabolic Anderson model in the plane.

Keywords: Integrated density of states; Anderson Hamiltonian; Parabolic Anderson model; White noise; Lifshitz tails; Self-intersection local time (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2022.07.007

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