Letters in Mathematical Physics

, Volume 72, Issue 1, pp 51–64 | Cite as

Fractional Moment Estimates for Random Unitary Operators

  • Alain Joye


We consider unitary analogs of d-dimensional Anderson models on l2( $$\mathbb(z)$$ d ) defined by the product Uω=Dω S where S is a deterministic unitary and Dω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman–Molchanov to get exponential estimates on fractional moments of the matrix elements of Uω(Uωz)−1, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of S. Such estimates imply almost sure localization for Uω.


fractional moment method unitary operators localization. 


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© Springer 2005

Authors and Affiliations

  • Alain Joye
    • 1
  1. 1.Institut FourierUniversité de Grenoble 1France

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