Some Estimates Regarding Integrated density of States for Random Schrödinger Operator with decaying Random Potentials

2015/01/21 by Dhriti Ranjan Dolai, Dolai, Dhriti Ranjan
Computer Science · Mathematics · #35J10 #35P20 #81Q10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP #msc:35J10 #msc:35P20 #msc:81Q10

paper · pdf · doi:10.48550/arxiv.1501.05055

openalex publication_date 2015/01/21 · arxiv created 2015/06/25 · arxiv updated 2015/06/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We investigate some bounds for the density of states in the pure point regime for the random Schrödinger operators H^ω=-Δ+∑_n∈ℤ^da_nq_n(ω), acting on ℓ²(ℤ^d), where \q_n\ are iid random variables and a_n≃|n|^-α~~α>0.

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