Central limit theorem for the random variables associated with the IDS of the Anderson model on the lattice
Dhriti Ranjan Dolai
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Source: Crossref
Published: Oct 26, 2026
DOI: 10.1142/s0129055x26610039
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We consider the existence of the integrated density of states (IDS) for the Anderson model on the Hilbert space [Formula: see text] as an analogue of the law of large numbers (LLN). In this work, we prove an analogue of the central limit theorem (CLT) for a collection of random variables associated with the integrated density of states, for the class of test functions [Formula: see text], consisting of all once-differentiable functions on the real line whose derivative is continuous and has at most polynomial growth. Our result extends the work of Grinshpon-White (J. Spectr. Theory 12 (2022) 591–615), where the CLT was established for polynomial test functions.
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