Paper Title:

Central limit theorem for the random variables associated with the IDS of the Anderson model on lattice

Published on:

14 September 2023

Primary Category:

Mathematical Physics

Paper Authors:

Dhriti Ranjan Dolai

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Proves central limit theorems for random variables linked to the integrated density of states of the Anderson model

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Theorems hold for test functions that are polynomials, infinitely smooth, and C1 with polynomial growth derivative

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Uses ergodic operators and probability inequalities like Markov and Chebyshev

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Shows the variance of the limiting normal distribution is positive for wide classes of test functions

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Applies to Anderson model on lattice in any dimension, improving on prior 1D results

Central limit theorem for random variables associated with the integrated density of states of the Anderson model

This paper proves central limit theorems for random variables associated with the integrated density of states of the Anderson model on a lattice. The theorems are shown for test functions that are polynomials, infinitely differentiable, and continuously differentiable with polynomial growth derivative. Key techniques involve ergodic operators and probability inequalities.

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