1,426 research outputs found
Probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension via a Monte-Carlo procedure in the disorder
In order to probe with high precision the tails of the ground-state energy
distribution of disordered spin systems, K\"orner, Katzgraber and Hartmann
\cite{Ko_Ka_Ha} have recently proposed an importance-sampling Monte-Carlo
Markov chain in the disorder. In this paper, we combine their Monte-Carlo
procedure in the disorder with exact transfer matrix calculations in each
sample to measure the negative tail of ground state energy distribution
for the directed polymer in a random medium of dimension .
In , we check the validity of the algorithm by a direct comparison with
the exact result, namely the Tracy-Widom distribution. In dimensions and
, we measure the negative tail up to ten standard deviations, which
correspond to probabilities of order . Our results are
in agreement with Zhang's argument, stating that the negative tail exponent
of the asymptotic behavior
as is directly related to the fluctuation exponent
(which governs the fluctuations
of the ground state energy for polymers of length ) via the simple
formula . Along the paper, we comment on the
similarities and differences with spin-glasses.Comment: 13 pages, 16 figure
Load factors for wind and snow loads for use in load resistance factor design criteria
This report presents the background and the derivations for the determination of the mean maximum loads and the corresponding load factors for wind and snow loading for use in Load and Resistance Factor Design Criteria for steel building structures
Tentative load and resistance factor design criteria for steel beam-columns
Nominal design equations and reai•tance factors are developed for steel beam-columns as part of Load and Resistance Factor Design criteria for steel buildings. The resistance factors are derived from principles of first-order probability theory using calibration to present designs
Fluctuating Fronts as Correlated Extreme Value Problems: An Example of Gaussian Statistics
In this paper, we view fluctuating fronts made of particles on a
one-dimensional lattice as an extreme value problem. The idea is to denote the
configuration for a single front realization at time by the set of
co-ordinates of the
constituent particles, where is the total number of particles in that
realization at time . When are arranged in the ascending order
of magnitudes, the instantaneous front position can be denoted by the location
of the rightmost particle, i.e., by the extremal value
. Due to interparticle
interactions, at two different times for a single front
realization are naturally not independent of each other, and thus the
probability distribution [based on an ensemble of such front
realizations] describes extreme value statistics for a set of correlated random
variables. In view of the fact that exact results for correlated extreme value
statistics are rather rare, here we show that for a fermionic front model in a
reaction-diffusion system, is Gaussian. In a bosonic front model
however, we observe small deviations from the Gaussian.Comment: 6 pages, 3 figures, miniscule changes on the previous version, to
appear in Phys. Rev.
A new test procedure of independence in copula models via chi-square-divergence
We introduce a new test procedure of independence in the framework of
parametric copulas with unknown marginals. The method is based essentially on
the dual representation of -divergence on signed finite measures. The
asymptotic properties of the proposed estimate and the test statistic are
studied under the null and alternative hypotheses, with simple and standard
limit distributions both when the parameter is an interior point or not.Comment: 23 pages (2 figures). Submitted to publicatio
Contest based on a directed polymer in a random medium
We introduce a simple one-parameter game derived from a model describing the
properties of a directed polymer in a random medium. At his turn, each of the
two players picks a move among two alternatives in order to maximize his final
score, and minimize opponent's return. For a game of length , we find that
the probability distribution of the final score develops a traveling wave
form, , with the wave profile unusually
decaying as a double exponential for large positive and negative . In
addition, as the only parameter in the game is varied, we find a transition
where one player is able to get his maximum theoretical score. By extending
this model, we suggest that the front velocity is selected by the nonlinear
marginal stability mechanism arising in some traveling wave problems for which
the profile decays exponentially, and for which standard traveling wave theory
applies
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