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Journal d’Analyse Mathématique

, Volume 96, Issue 1, pp 313–355 | Cite as

Positivity and continuity of the Lyapounov exponent for shifts on T d with arbitrary frequency vector and real analytic potentiald with arbitrary frequency vector and real analytic potential

  • J. Bourgain
Article

Keywords

Harmonic Measure Subharmonic Function Shift Vector Anderson Localization Apply Lemma 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [B] J. Bourgain,Green’s function estimates for lattice Schrödinger operators and applications, Ann. of Math. Stud.158, Princeton University Press, 2005.Google Scholar
  2. [B-G] J. Bourgain and M. Goldstein,On nonperturbative localization with quasiperiodic potential, Ann. of Math. (2)152 (2000), 835–879.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [B-G-S] J. Bourgain, M. Goldstein and W. Schlag,Anderson, localization for Schrödinger operators on Z with potentials given by the skew-shift, Comm. Math. Phys.220 (2001), 583–621.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [B-J] J. Bourgain and S. Jitomirskaya,Continuity of the Lyapounov exponent for quasiperiodic operators with analytic potential, J. Statist. Phys.108 (2002), 1203–1218.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [G-S] M. Goldstein and W. Schlag,Hölder continuity of the integrated density of states for quasiperiodic Schrödinger operators and averages for shifts of subharmonic functions, Ann. of Math. (2)154 (2001), 155–203.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [S-S] E. Sorets and T. Spencer,Positive Lyapounov exponents for Schrödinger operators with quasi-periodic potentials, Comm. Math. Phys.142 (1991), 543–566.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© The Hebrew University Magnes Press 2005

Authors and Affiliations

  • J. Bourgain
    • 1
  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA

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