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• W2949012011 abstract "We establish precise asymptotics near zero of the integrated density of states for the random Schrodinger operators $(-Delta)^{alpha/2} + V^{omega}$ in $L^2(mathbb R^d)$ for the full range of $alphain(0,2]$ and a fairly large class of random nonnegative alloy-type potentials $V^{omega}$. The IDS exhibits the Lifschitz tail singularity. We prove the existence of the limit $$lim_{sto 0} s^{d/alpha}lnell([0,s]) = -C left(lambda_d^{(alpha)}right)^{d/alpha},$$ with $C in (0,infty]$. The constant $C$ is is finite if and only if the common distribution of the lattice random variables charges $left{0right}$. In this case, the constant $C$ is expressed explicitly in terms of such a probability. In the limit formula, $lambda_d^{(alpha)}$ denotes the Dirichlet ground-state eigenvalue of the operator $(-Delta)^{alpha/2}$ in the unit ball in $mathbb R^d.$" @default.
• W2949012011 created "2019-06-14" @default.
• W2949012011 creator A5012302532 @default.
• W2949012011 creator A5079549507 @default.
• W2949012011 date "2019-06-08" @default.
• W2949012011 modified "2023-09-26" @default.
• W2949012011 title "Lifschitz tail for alloy-type models driven by the fractional Laplacian" @default.
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