1,332 research outputs found
Concentration of empirical distribution functions with applications to non-i.i.d. models
The concentration of empirical measures is studied for dependent data, whose
joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev
inequalities. The general concentration results are then applied to spectral
empirical distribution functions associated with high-dimensional random
matrices.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ254 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Equilibrium route to colloidal gellation: mixtures of hard sphere-like colloids
The binodals and the non-ergodicity lines of a binary mixture of hard
sphere-like particles with large size ratio are computed for studying the
interplay between dynamic arrest and phase separation in depletion-driven
colloidal mixtures. Contrarily to the case of hard core plus short range
effective attraction, physical gellation without competition with the
fluid-phase separation can occur in such mixtures. This behavior due to the
oscillations in the depletion potential should concern all simple mixtures with
non-ideal depletant, justifying further studies of their dynamic properties
Glass Dynamics at High Strain Rates
We present a shear-transformation-zone (STZ) theoretical analysis of
molecular-dynamics simulations of a rapidly sheared metallic glass. These
simulations are especially revealing because, although they are limited to high
strain rates, they span temperatures ranging from well below to well above the
glass transition. With one important discrepancy, the STZ theory reproduces the
simulation data, including the way in which those data can be made to collapse
onto simple curves by a scaling transformation. The STZ analysis implies that
the system's behavior at high strain rates is controlled primarily by
effective-temperature thermodynamics, as opposed to system-specific details of
the molecular interactions. The discrepancy between theory and simulations
occurs at the lower strain rates for temperatures near the glass transition. We
argue that this discrepancy can be resolved by the same multi-species
generalization of STZ theory that has been proposed recently for understanding
frequency-dependent viscoelastic responses, Stokes-Einstein violations, and
stretched-exponential relaxation in equilibrated glassy materials.Comment: 9 pages, 6 figure
Vibrational origin of the fast relaxation processes in molecular glass-formers
We study the interaction of the relaxation processes with the density
fluctuations by molecular dynamics simulation of a flexible molecule model for
o-terphenyl (oTP) in the liquid and supercooled phases. We find evidence,
besides the structural relaxation, of a secondary vibrational relaxation whose
characteristic time, few ps, is slightly temperature dependent. This i)
confirms the result by Monaco et al. [Phys. Rev, E 62, 7595 (2000)] of the
vibrational nature of the fast relaxation observed in Brillouin Light
Scattering (BLS) experiments in oTP; and ii) poses a caveat on the
interpretation of the BLS spectra of molecular systems in terms of a purely
center of mass dynamics.Comment: RevTeX, 5 pages, 4 eps figure
Arak Inequalities for Concentration Functions and the Littlewood--Offord Problem: a shortened version
Let be independent identically distributed random
variables. In this paper we study the behavior of concentration functions of
weighted sums with respect to the arithmetic structure
of coefficients~ in the context of the Littlewood--Offord problem.
Concentration results of this type received renewed interest in connection with
distributions of singular values of random matrices. Recently, Tao and Vu
proposed an Inverse Principle in the Littlewood--Offord problem. We discuss the
relations between the Inverse Principle of Tao and Vu as well as that of Nguyen
and Vu and a similar principle formulated for sums of arbitrary independent
random variables in the work of Arak from the 1980's. This paper is a shortened
and edited version of the preprint arXiv:1506.09034. Here we present the
results without proofs.Comment: 9 pages. shortened version of arXiv:1506.0903
Convergence to Stable Laws in Relative Entropy
Convergence to stable laws in relative entropy is established for sums of
i.i.d. random variables
The mean-squared displacement of a molecule moving in a glassy system
The mean-squared displacement (MSD) of a hard sphere and of a dumbbell
molecule consisting of two fused hard spheres immersed in a dense hard-sphere
system is calculated within the mode-coupling theory for ideal liquid-glass
transitions. It is proven that the velocity correlator, which is the second
time derivative of the MSD, is the negative of a completely monotone function
for times within the structural-relaxation regime. The MSD is found to exhibit
a large time interval for structural relaxation prior to the onset of the
-process which cannot be described by the asymptotic formulas for the
mode-coupling-theory-bifurcation dynamics. The -process for molecules
with a large elongation is shown to exhibit an anomalously wide cross-over
interval between the end of the von-Schweidler decay and the beginning of
normal diffusion. The diffusivity of the molecule is predicted to vary
non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin
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