45,095 research outputs found
-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity
We study spectral properties of Schr\"odinger operators on \RR^d. The
electromagnetic potential is assumed to be determined locally by a colouring of
the lattice points in \ZZ^d, with the property that frequencies of finite
patterns are well defined. We prove that the integrated density of states
(spectral distribution function) is approximated by its finite volume
analogues, i.e.the normalised eigenvalue counting functions. The convergence
holds in the space where is any finite energy interval and is arbitrary.Comment: 15 pages; v2 has minor fixe
On Gaussian multiplicative chaos
We propose a new definition of the Gaussian multiplicative chaos (GMC) and an
approach based on the relation of subcritical GMC to randomized shifts of a
Gaussian measure. Using this relation we prove general uniqueness and
convergence results for subcritical GMC that hold for Gaussian fields with
arbitrary covariance kernels.Comment: 34 pages. Major revision of the original version. Numeration has
changed significantl
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