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4:00 pm Wednesday, November 6, 2013 Stulken Lecture: Gaps Between Eigenvalues of Quasi-Periodic SchrÃ¶dinger Operators IIby Michael Goldstein (University of Toronto) in HB 227- This is the second talk in the four lectures series on the size of the splitting between eigenvalues of quasi-periodic Schrodinger equation. In this lecture we will discuss so-called avalanche principle and the way it works in combination with large deviation theorem. We will see how this combination allows to sharpen the estimates on the deviations of the logarithm of the fundamental matrix due to the second application of the subharmonicity of this logarithm as a function of phase. We will see how to translate the information from the fundamental matrix to its entries and how this allows to estimate the number of complexified phase zeros of the characteristic polynomial of the problem at fixed values of the spectral parameter.
Submitted by damanik@rice.edu |