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Poisson-Type Limit Theorems for Eigenvalues of Finite-Volume Anderson Hamiltonians
We consider the spectral problem for the random Schrödinger operator on the multidimensional lattice torus increasing to the whole of lattice, with an i.i.d. potential (Anderson Hamiltonian). We prove complet...
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Strong laws for exponential order statistics and spacings
We obtain upper and lower almost sure asymptotic bounds for spacings η K, N − η K + 1, N , where η ...
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Article
On High-Level Exceedances of Gaussian Fields and the Spectrum of Random Hamiltonians
We study the almost sure asymptotic structure of high-level exceedances by Gaussian random field ξ(x), x∈V with correlated values, where {V} is a family of ν-dimensional cubes increasing to Z ν. The results are a...
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Article
Limit theorems for the maximal eigenvalues of the mean-field Hamiltonian with random potential
Let \(\bar H_V = \kappa \bar \Delta _V + \xi _V (x),x \in V \subset \mathbb{Z}^v \) , be the mean-field Hamiltonian...
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Limit theorems for basic states of the anderson model
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Article
The asymptotic dependence structure of the linear fractional Lévy motion
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Limit theorem for a random walk in a reversible random environment
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Limit theorems for a random walk in a random environment
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Limit theorems for a random walk in a random environment
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Limit theorems for quadratic forms of linear processes
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Limit theorems for sums of linearly generated random variables
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Stable self-similar fields