Spectral Statistics for one dimensional Anderson model with unbounded\n but decaying potential

2016/02/09 by Anish Mallick, Mallick, Anish, Dhriti Ranjan Dolai +1
Computer Science · Mathematics · Physics and Astronomy · #34L20 #35J10 #81Q10 #82B44 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1602.02986

openalex publication_date 2016/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we study the spectral statistics for Anderson model on\n\ℓ²(\ℕ) with decaying randomness whose single site distribution\nhas unbounded support. Here we consider the operator H^\ω given by\n(H^\ω u)_n=u_n+1+u_n-1+a_n\ω_n u_n, a_n\∼ n^-\α and\n \ω_n are real i.i.d random variables following symmetric distribution\n\μ with fat tail, i.e \μ((-R,R)^c)<\(C)/(R^\δ) for R\≫ 1, for\nsome constant C. In case of \α-\(1)/(\δ)>\(1)/(2), we are\nable to show that the eigenvalue process in (-2,2) is the clock process.\n

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