Mathematics and Statistics Vol. 1(3), pp. 119 - 134
DOI: 10.13189/ms.2013.010304
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Lyapunov Exponents and Large Deviations Analysis of Eigenfunctions in Anderson Models on Graphs

VICTOR CHULAEVSKY^*
Departement De Mathematiques Universite De Reims, Moulin De La Housse, B.P. 1039 51687 Reims, Cedex 2, France

ABSTRACT

We propose a new probabilistic approach to the analysis of decay of the Green’s functions and the eigenfunctions of the Anderson Hamiltonians on countable graphs. Our method is close in spirit to the Fractional Moment Method, but we show how the use of the fractional moments can be avoided, so that exponential decay of the Green’s functions can be established in some models where the fractional moments diverge, due to low regularity of the random potential. We elucidate the exceptional role of the Holder continuity condition, usual in the FMM, in terms of Cramer’s condition in the large deviations problem for a suitably constructed rigorous path expansion.

KEYWORDS
Anderson Localization, Schur Complement, Large Deviations Estimates

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] VICTOR CHULAEVSKY , "Lyapunov Exponents and Large Deviations Analysis of Eigenfunctions in Anderson Models on Graphs," Mathematics and Statistics, Vol. 1, No. 3, pp. 119 - 134, 2013. DOI: 10.13189/ms.2013.010304.

(b). APA Format:
VICTOR CHULAEVSKY (2013). Lyapunov Exponents and Large Deviations Analysis of Eigenfunctions in Anderson Models on Graphs. Mathematics and Statistics, 1(3), 119 - 134. DOI: 10.13189/ms.2013.010304.