## Abstract

We consider random self-adjoint Jacobi matrices of the form. on ℓ^{2}(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 J_{p} be the deterministic periodic (of period q) Jacobi matrix whose coefficients are the mean values of the corresponding entries in J_{ω}. We prove that for a.e. ω, the a.c. spectrum of the operator J_{ω} equals to and fills the spectrum of J_{p}. If, moreover,. then for a.e. ω, the spectrum of J_{ω} is purely absolutely continuous on the interior of the bands that make up the spectrum of Jp.

Original language | English |
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Pages (from-to) | 1029-1044 |

Number of pages | 16 |

Journal | Journal of Functional Analysis |

Volume | 260 |

Issue number | 4 |

DOIs | |

State | Published - 28 Feb 2011 |

### Bibliographical note

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.

## Keywords

- Absolutely continuous spectrum
- Random Jacobi matrices