TY - JOUR
T1 - Spectral and dynamical properties of certain random jacobi matrices with growing parameters
AU - Breuer, Jonathan
PY - 2010/6
Y1 - 2010/6
N2 - In this paper, a family of random Jacobi matrices with off-diagonal terms that exhibit power-law growth is studied. Since the growth of the randomness is slower than that of these terms, it is possible to use methods applied in the study of Schrödinger operators with random decaying potentials. A particular result of the analysis is the existence of operators with arbitrarily fast transport whose spectral measure is zero dimensional. The results are applied to the infinite Dumitriu-Edelman model (2002), and its spectral properties are analyzed.
AB - In this paper, a family of random Jacobi matrices with off-diagonal terms that exhibit power-law growth is studied. Since the growth of the randomness is slower than that of these terms, it is possible to use methods applied in the study of Schrödinger operators with random decaying potentials. A particular result of the analysis is the existence of operators with arbitrarily fast transport whose spectral measure is zero dimensional. The results are applied to the infinite Dumitriu-Edelman model (2002), and its spectral properties are analyzed.
UR - http://www.scopus.com/inward/record.url?scp=77951625544&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-10-04856-7
DO - 10.1090/S0002-9947-10-04856-7
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AN - SCOPUS:77951625544
SN - 0002-9947
VL - 362
SP - 3161
EP - 3182
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 6
ER -