94,274 research outputs found
Burgess-like subconvex bounds for
We give a Burgess-like subconvex bound for in terms
of the analytical conductor of , where is a cuspidal
representation and is a Hecke character.Comment: to appear in Geometric and Functional Analysi
Ehrenfest breakdown of the mean-field dynamics of Bose gases
The mean-field dynamics of a Bose gas is shown to break down at time where is the Lyapunov exponent of the mean-field
theory, is the number of bosons, and is a system-dependent constant.
The breakdown time is essentially the Ehrenfest time that
characterizes the breakdown of the correspondence between classical and quantum
dynamics. This breakdown can be well described by the quantum fidelity defined
for reduced density matrices. Our results are obtained with the formalism in
particle-number phase space and are illustrated with a triple-well model. The
logarithmic quantum-classical correspondence time may be verified
experimentally with Bose-Einstein condensates.Comment: 6 pages, 4 figure
Covariance matrix estimation for stationary time series
We obtain a sharp convergence rate for banded covariance matrix estimates of
stationary processes. A precise order of magnitude is derived for spectral
radius of sample covariance matrices. We also consider a thresholded covariance
matrix estimator that can better characterize sparsity if the true covariance
matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911)
351-376] idea and relate eigenvalues of covariance matrices to the spectral
densities or Fourier transforms of the covariances. We develop a large
deviation result for quadratic forms of stationary processes using m-dependence
approximation, under the framework of causal representation and physical
dependence measures.Comment: Published in at http://dx.doi.org/10.1214/11-AOS967 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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