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We study two systems that are based on sums of weakly dependent
Bernoulli random variables that take values ± 1 with equal
probabilities. We show that already one step of the so-called
soft decision parallel interference cancellation, used in the third
generation of mobile telecommunication CDMA, is able to considerably
increase the number of users such a system can host. We also
consider a variant of the well-known Hopfield model of neural
networks. We show that this variant proposed by Amari...
We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than
and obeys some natural regularity conditions.
Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption
that a small set of fields provides a closed description on large space and time scales.
Conditions governing the choice for these fields are discussed in the context of granular
fluids and multi-component fluids. In the first case, the relevance of temperature or
energy as a hydrodynamic field is justified. For mixtures, the use of a total temperature
and single...
In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly affects...
The primary objective of this work is to develop coarse-graining
schemes for stochastic many-body microscopic models and quantify their
effectiveness in terms of a priori and a posteriori error analysis. In
this paper we focus on stochastic lattice systems of
interacting particles at equilibrium.
The proposed algorithms are derived from an initial coarse-grained
approximation that is directly computable by Monte Carlo simulations,
and the corresponding numerical error is calculated using the...
New experiments on neutral K-mesons might turn out to be promising tests of the hypothesis of Complete Positivity in the physics of open quantum systems. In particular, a consistent dynamical description of correlated neutral kaons seems to ask for Complete Positivity.
This paper describes the extension of a
recently developed numerical solver for the Landau-Lifshitz
Navier-Stokes (LLNS) equations to binary mixtures in three
dimensions. The LLNS equations incorporate thermal fluctuations into
macroscopic hydrodynamics by using white-noise fluxes. These
stochastic PDEs are more complicated in three dimensions due to the
tensorial form of the correlations for the stochastic fluxes and in
mixtures due to couplings of energy and concentration fluxes (e.g.,
Soret...
The model of random interlacements on ℤd, d≥3, was recently introduced in [Vacant set of random interlacements and percolation. Available at http://www.math.ethz.ch/u/sznitman/preprints]. A non-negative parameter u parametrizes the density of random interlacements on ℤd. In the present note we investigate connectivity properties of the vacant set left by random interlacements at level u, in the non-percolative regime u>u∗, with u∗ the non-degenerate critical parameter for the percolation...
We show that Boltzmann's collision operator can be written explicitly
in divergence and double divergence forms. These conservative
formulations may be of interest for both theoretical and numerical
purposes. We give an application to the asymptotics of grazing
collisions.
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