14,734 research outputs found
Asymptotic results for sums and extremes
The term moderate deviations is often used in the literature to mean a class
of large deviation principles that, in some sense, fills the gap between a
convergence in probability of some random variables to a constant and a weak
convergence to a centered Gaussian distribution (when such random variables are
properly centered and rescaled). We talk about noncentral moderate deviations
when the weak convergence is towards a non-Gaussian distribution. In this
paper, we prove a noncentral moderate deviation result for the bivariate
sequence of sums and maxima of i.i.d. random variables bounded from above. We
also prove a result where the random variables are not bounded from above, and
the maxima are suitably normalized. Finally, we prove a moderate deviation
result for sums of partial minima of i.i.d. exponential random variables.Comment: 1
Phase separation of a multiple occupancy lattice gas
A binary lattice gas model that allows for multiple occupancy of lattice
sites, inspired by recent coarse-grained descriptions of solutions of
interacting polymers, is investigated by combining the steepest descent
approximation with an exploration of the multidimensional energy landscape, and
by Gibbs ensemble Monte Carlo simulations. The one-component version of the
model, involving on site and nearest neighbour interactions, is shown to
exhibit microphase separation into two sub-lattices with different mean
occupation numbers. The symmetric two-component version of the multiple
occupancy lattice gas is shown to exhibit a demixing transition into two phases
above a critical mean occupation number.Comment: submitted to Journal of Physics
Spectra: Robust Estimation of Distribution Functions in Networks
Distributed aggregation allows the derivation of a given global aggregate
property from many individual local values in nodes of an interconnected
network system. Simple aggregates such as minima/maxima, counts, sums and
averages have been thoroughly studied in the past and are important tools for
distributed algorithms and network coordination. Nonetheless, this kind of
aggregates may not be comprehensive enough to characterize biased data
distributions or when in presence of outliers, making the case for richer
estimates of the values on the network. This work presents Spectra, a
distributed algorithm for the estimation of distribution functions over large
scale networks. The estimate is available at all nodes and the technique
depicts important properties, namely: robust when exposed to high levels of
message loss, fast convergence speed and fine precision in the estimate. It can
also dynamically cope with changes of the sampled local property, not requiring
algorithm restarts, and is highly resilient to node churn. The proposed
approach is experimentally evaluated and contrasted to a competing state of the
art distribution aggregation technique.Comment: Full version of the paper published at 12th IFIP International
Conference on Distributed Applications and Interoperable Systems (DAIS),
Stockholm (Sweden), June 201
Discrete structure of ultrathin dielectric films and their surface optical properties
The boundary problem of linear classical optics about the interaction of
electromagnetic radiation with a thin dielectric film has been solved under
explicit consideration of its discrete structure. The main attention has been
paid to the investigation of the near-zone optical response of dielectrics. The
laws of reflection and refraction for discrete structures in the case of a
regular atomic distribution are studied and the structure of evanescent
harmonics induced by an external plane wave near the surface is investigated in
details. It is shown by means of analytical and numerical calculations that due
to the existence of the evanescent harmonics the laws of reflection and
refraction at the distances from the surface less than two interatomic
distances are principally different from the Fresnel laws. From the practical
point of view the results of this work might be useful for the near-field
optical microscopy of ultrahigh resolution.Comment: 25 pages, 16 figures, LaTeX2.09, to be published in Phys.Rev.
Magnetic moment of an electron gas on the surface of constant negative curvature
The magnetic moment of an electron gas on the surface of constant negative
curvature is investigated. It is shown that the surface curvature leads to the
appearance of the region of the monotonic dependence at low magnetic
fields. At high magnetic fields, the dependence of the magnetic moment on a
magnetic field is the oscillating one. The effect of the surface curvature is
to increase the region of the monotonic dependence of the magnetic moment and
to break the periodicity of oscillations of the magnetic moment as a function
of an inverse magnetic field.Comment: 4 pages, 1 figur
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