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Jakšić–Last theorem for higher rank perturbations
Authors:Anish Mallick
Affiliation:The Institute of Mathematical Sciences, Chennai, Tamil Nadu, India
Abstract:We consider the generalized Anderson model urn:x-wiley:0025584X:media:mana201400423:mana201400423-math-0001, where urn:x-wiley:0025584X:media:mana201400423:mana201400423-math-0002 is a countable set, urn:x-wiley:0025584X:media:mana201400423:mana201400423-math-0003 are i.i.d. random variables and the urn:x-wiley:0025584X:media:mana201400423:mana201400423-math-0004 are rank urn:x-wiley:0025584X:media:mana201400423:mana201400423-math-0005 projections. For these models we prove theorem analogous to that of Jak?i?–Last on the equivalence of the trace measure urn:x-wiley:0025584X:media:mana201400423:mana201400423-math-0006 for urn:x-wiley:0025584X:media:mana201400423:mana201400423-math-0007 a.e. ω. Our model covers the dimer and polymer models.
Keywords:Spectral theory  Anderson model  perturbation theory  47A10  47A55  47B25  82B44  60H25  81Q10
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