11,991 research outputs found
The Dynamic Range of LZ
The electronics of the LZ experiment, the 7-tonne dark matter detector to be
installed at the Sanford Underground Research Facility (SURF), is designed to
permit studies of physics where the energies deposited range from 1 keV of
nuclear-recoil energy up to 3,000 keV of electron-recoil energy. The system is
designed to provide a 70% efficiency for events that produce three
photoelectrons in the photomultiplier tubes (PMTs). This corresponds
approximately to the lowest energy threshold achievable in multi-tonne
time-projection chambers, and drives the noise specifications for the front
end. The upper limit of the LZ dynamic range is defined to accommodate the
electroluminescence (S2) signals. The low-energy channels of the LZ amplifiers
provide the dynamic range required for the tritium and krypton calibrations.
The high-energy channels provide the dynamic range required to measure the
activated Xe lines
The outliers of a deformed Wigner matrix
We derive the joint asymptotic distribution of the outlier eigenvalues of an
additively deformed Wigner matrix . Our only assumptions on the deformation
are that its rank be fixed and its norm bounded. Our results extend those of
[The isotropic semicircle law and deformation of Wigner matrices. Preprint] by
admitting overlapping outliers and by computing the joint distribution of all
outliers. In particular, we give a complete description of the failure of
universality first observed in [Ann. Probab. 37 (2009) 1-47; Ann. Inst. Henri
Poincar\'{e} Probab. Stat. 48 (1013) 107-133; Free convolution with a
semi-circular distribution and eigenvalues of spiked deformations of Wigner
matrices. Preprint]. We also show that, under suitable conditions, outliers may
be strongly correlated even if they are far from each other. Our proof relies
on the isotropic local semicircle law established in [The isotropic semicircle
law and deformation of Wigner matrices. Preprint]. The main technical
achievement of the current paper is the joint asymptotics of an arbitrary
finite family of random variables of the form
.Comment: Published in at http://dx.doi.org/10.1214/13-AOP855 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Eigenvector Distribution of Wigner Matrices
We consider Hermitian or symmetric random matrices with
independent entries. The distribution of the -th matrix element is given
by a probability measure whose first two moments coincide with those
of the corresponding Gaussian ensemble. We prove that the joint probability
distribution of the components of eigenvectors associated with eigenvalues
close to the spectral edge agrees with that of the corresponding Gaussian
ensemble. For eigenvectors associated with bulk eigenvalues, the same
conclusion holds provided the first four moments of the distribution
coincide with those of the corresponding Gaussian ensemble. More generally, we
prove that the joint eigenvector-eigenvalue distributions near the spectral
edge of two generalized Wigner ensembles agree, provided that the first two
moments of the entries match and that one of the ensembles satisfies a level
repulsion estimate. If in addition the first four moments match then this
result holds also in the bulk
A Lower Bound on the Ground State Energy of Dilute Bose Gas
Consider an N-Boson system interacting via a two-body repulsive short-range
potential in a three dimensional box of side length . We take
the limit while keeping the density fixed
and small. We prove a new lower bound for its ground state energy per particle
as , where is the scattering length of .Comment: 26 pages, AMS LaTe
- β¦