|
Spectral localization in the hierarchical Anderson model
Author(s):
Evgenij
Kritchevski
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1431-1440.
MSC (2000):
Primary 47B80, 47A55, 93A13.
Posted:
November 13, 2006
MathSciNet review:
2276652
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove that a large class of hierarchical Anderson models with spectral dimension  has only pure point spectrum.
References:
-
- [AM]
- Aizenman, M., Molchanov, S.: Localization at large disorder and at extreme energies: an elementary derivation. Commun. Math. Phys. 157 (1993), no. 2, 245-278. MR 1244867 (95a:82052)
- [Bo]
- Bovier, A.: The density of states in the Anderson model at weak disorder: a renormalization group analysis of the hierarchical model. J. Statist. Phys. 59 (1990), no. 3-4, 745-779. MR 1063180 (91m:82063)
- [BS]
- Bleher, P. M., Sinai, Ya. G.: Investigation of the Critical Point in Models of the Type of Dyson's Hierarchical Models. Commun. Math. Phys. 33, (1973).
- [DMS]
- del Rio, R., Makarov, N., Simon, B.: Operators with singular continuous spectrum: II. Rank one operators. Commun. Math. Phys. 165 (1994), 59. MR 1298942 (97a:47002)
- [D]
- Dyson, F.J.: Existence of a phase-transition in a one dimensional Ising Ferromagnet. Comm. Math. Phys. 12, 91 (1969). MR 0436850 (55:9786)
- [G]
- Gordon, A.: Pure point spectrum under 1-parameter perturbations and instability of Anderson localization. Commun. Math. Phys. 164 (1994), 489. MR 1291242 (95k:47019)
- [M1]
- Molchanov, S.: Lectures on random media. Lectures on probability theory (Saint-Flour, 1992), 242-411, Lecture Notes in Math., 1581, Springer, Berlin, 1994. MR 1307415 (95m:60165)
- [M2]
- Molchanov, S.: Hierarchical random matrices and operators. Application to Anderson model. Multidimensional statistical analysis and theory of random matrices (Bowling Green, OH, 1996), 179-194, VSP, Utrecht, 1996.MR 1463464 (99b:82054)
- [SW]
- Simon, B., Wolff, T.: Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Communications in Pure and Applied Mathematics 49 (1986), 75. MR 0820340 (87k:47032)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
47B80, 47A55, 93A13.
Retrieve articles in all Journals with
MSC (2000):
47B80, 47A55, 93A13.
Additional Information:
Evgenij
Kritchevski
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6
Email:
ekritc@math.mcgill.ca
DOI:
10.1090/S0002-9939-06-08614-X
PII:
S 0002-9939(06)08614-X
Received by editor(s):
December 8, 2005
Posted:
November 13, 2006
Additional Notes:
This work was supported in part by an FQRNT grant.
Communicated by:
Mikhail Shubin
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
