TY - JOUR
T1 - Preservation of a.c. spectrum for random decaying perturbations of square-summable high-order variation
AU - Kaluzhny, Uri
AU - Last, Yoram
N1 - Funding Information: We would like to thank J. Breuer, M. Shamis, and B. Simon for useful discussions. This research was supported in part by The Israel Science Foundation (Grant No. 1169/06) and by Grant 2006483 from the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel.
PY - 2011/2/28
Y1 - 2011/2/28
N2 - We consider random self-adjoint Jacobi matrices of the form. on ℓ2(N), where {an(ω)>0} and {bn(ω)∈R} are sequences of random variables on a probability space (ω,dP(ω)) such that there exists q∈N, such that for any l∈N,. are independent random variables of zero mean satisfying. Let Jp be the deterministic periodic (of period q) Jacobi matrix whose coefficients are the mean values of the corresponding entries in Jω. We prove that for a.e. ω, the a.c. spectrum of the operator Jω equals to and fills the spectrum of Jp. If, moreover,. then for a.e. ω, the spectrum of Jω is purely absolutely continuous on the interior of the bands that make up the spectrum of Jp.
AB - We consider random self-adjoint Jacobi matrices of the form. on ℓ2(N), where {an(ω)>0} and {bn(ω)∈R} are sequences of random variables on a probability space (ω,dP(ω)) such that there exists q∈N, such that for any l∈N,. are independent random variables of zero mean satisfying. Let Jp be the deterministic periodic (of period q) Jacobi matrix whose coefficients are the mean values of the corresponding entries in Jω. We prove that for a.e. ω, the a.c. spectrum of the operator Jω equals to and fills the spectrum of Jp. If, moreover,. then for a.e. ω, the spectrum of Jω is purely absolutely continuous on the interior of the bands that make up the spectrum of Jp.
KW - Absolutely continuous spectrum
KW - Random Jacobi matrices
UR - http://www.scopus.com/inward/record.url?scp=78650305791&partnerID=8YFLogxK
U2 - https://doi.org/10.1016/j.jfa.2010.05.014
DO - https://doi.org/10.1016/j.jfa.2010.05.014
M3 - Article
SN - 0022-1236
VL - 260
SP - 1029
EP - 1044
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 4
ER -