67 research outputs found
Multi-scale homogenization with bounded ratios and Anomalous Slow Diffusion
We show that the effective diffusivity matrix for the heat operator
in a periodic potential
obtained as a superposition of Holder-continuous
periodic potentials (of period \T^d:=\R^d/\Z^d, ,
) decays exponentially fast with the number of scales when the
scale-ratios are bounded above and below. From this we deduce the
anomalous slow behavior for a Brownian Motion in a potential obtained as a
superposition of an infinite number of scales: Comment: 29 pages, 1 figure, submitted versio
Scaling limit for trap models on
We give the ``quenched'' scaling limit of Bouchaud's trap model in . This scaling limit is the fractional-kinetics process, that is the time
change of a -dimensional Brownian motion by the inverse of an independent
-stable subordinator.Comment: Published in at http://dx.doi.org/10.1214/009117907000000024 the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Smallest Singular Value for Perturbations of Random Permutation Matrices
We take a first small step to extend the validity of Rudelson-Vershynin type
estimates to some sparse random matrices, here random permutation matrices. We
give lower (and upper) bounds on the smallest singular value of a large random
matrix D+M where M is a random permutation matrix, sampled uniformly, and D is
diagonal. When D is itself random with i.i.d terms on the diagonal, we obtain a
Rudelson-Vershynin type estimate, using the classical theory of random walks
with negative drift.Comment: 33 page
Extreme gaps between eigenvalues of random matrices
This paper studies the extreme gaps between eigenvalues of random matrices.
We give the joint limiting law of the smallest gaps for Haar-distributed
unitary matrices and matrices from the Gaussian unitary ensemble. In
particular, the kth smallest gap, normalized by a factor , has a
limiting density proportional to . Concerning the largest
gaps, normalized by , they converge in to a
constant for all . These results are compared with the extreme gaps
between zeros of the Riemann zeta function.Comment: Published in at http://dx.doi.org/10.1214/11-AOP710 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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