18,825 research outputs found
Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure
In [arXiv:0804.3035] we studied an interacting particle system which can be
also interpreted as a stochastic growth model. This model belongs to the
anisotropic KPZ class in 2+1 dimensions. In this paper we present the results
that are relevant from the perspective of stochastic growth models, in
particular: (a) the surface fluctuations are asymptotically Gaussian on a
sqrt(ln(t)) scale and (b) the correlation structure of the surface is
asymptotically given by the massless field.Comment: 13 pages, 4 figure
Universality of slow decorrelation in KPZ growth
There has been much success in describing the limiting spatial fluctuations
of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper
rescaling of time should introduce a non-trivial temporal dimension to these
limiting fluctuations. In one-dimension, the KPZ class has the dynamical
scaling exponent , that means one should find a universal space-time
limiting process under the scaling of time as , space like
and fluctuations like as .
In this paper we provide evidence for this belief. We prove that under
certain hypotheses, growth models display temporal slow decorrelation. That is
to say that in the scalings above, the limiting spatial process for times and are identical, for any . The hypotheses are known
to be satisfied for certain last passage percolation models, the polynuclear
growth model, and the totally / partially asymmetric simple exclusion process.
Using slow decorrelation we may extend known fluctuation limit results to
space-time regions where correlation functions are unknown.
The approach we develop requires the minimal expected hypotheses for slow
decorrelation to hold and provides a simple and intuitive proof which applied
to a wide variety of models.Comment: Exposition improved, typos correcte
Mean Field Voter Model of Election to the House of Representatives in Japan
In this study, we propose a mechanical model of a plurality election based on
a mean field voter model. We assume that there are three candidates in each
electoral district, i.e., one from the ruling party, one from the main
opposition party, and one from other political parties. The voters are
classified as fixed supporters and herding (floating) voters with ratios of
and , respectively. Fixed supporters make decisions based on their
information and herding voters make the same choice as another randomly
selected voter. The equilibrium vote-share probability density of herding
voters follows a Dirichlet distribution. We estimate the composition of fixed
supporters in each electoral district and using data from elections to the
House of Representatives in Japan (43rd to 47th). The spatial inhomogeneity of
fixed supporters explains the long-range spatial and temporal correlations. The
estimated values of are close to the estimates obtained from a survey.Comment: 11 pages, 7 figure
From interacting particle systems to random matrices
In this contribution we consider stochastic growth models in the
Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large
time distribution and processes and their dependence on the class on initial
condition. This means that the scaling exponents do not uniquely determine the
large time surface statistics, but one has to further divide into subclasses.
Some of the fluctuation laws were first discovered in random matrix models.
Moreover, the limit process for curved limit shape turned out to show up in a
dynamical version of hermitian random matrices, but this analogy does not
extend to the case of symmetric matrices. Therefore the connections between
growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor
corrections in scaling of section 2.
On the asymmetric zero-range in the rarefaction fan
We consider the one-dimensional asymmetric zero-range process starting from a
step decreasing profile. In the hydrodynamic limit this initial condition leads
to the rarefaction fan of the associated hydrodynamic equation. Under this
initial condition and for totally asymmetric jumps, we show that the weighted
sum of joint probabilities for second class particles sharing the same site is
convergent and we compute its limit. For partially asymmetric jumps we derive
the Law of Large Numbers for the position of a second class particle under the
initial configuration in which all the positive sites are empty, all the
negative sites are occupied with infinitely many first class particles and with
a single second class particle at the origin. Moreover, we prove that among the
infinite characteristics emanating from the position of the second class
particle, this particle chooses randomly one of them. The randomness is given
in terms of the weak solution of the hydrodynamic equation through some sort of
renormalization function. By coupling the zero-range with the exclusion process
we derive some limiting laws for more general initial conditions.Comment: 22 pages, to appear in Journal of Statistical Physic
Particle Systems with Stochastic Passing
We study a system of particles moving on a line in the same direction.
Passing is allowed and when a fast particle overtakes a slow particle, it
acquires a new velocity drawn from a distribution P_0(v), while the slow
particle remains unaffected. We show that the system reaches a steady state if
P_0(v) vanishes at its lower cutoff; otherwise, the system evolves
indefinitely.Comment: 5 pages, 5 figure
Small-sample corrections for score tests in Birnbaum-Saunders regressions
In this paper we deal with the issue of performing accurate small-sample
inference in the Birnbaum-Saunders regression model, which can be useful for
modeling lifetime or reliability data. We derive a Bartlett-type correction for
the score test and numerically compare the corrected test with the usual score
test, the likelihood ratio test and its Bartlett-corrected version. Our
simulation results suggest that the corrected test we propose is more reliable
than the other tests.Comment: To appear in the Communications in Statistics - Theory and Methods,
http://www.informaworld.com/smpp/title~content=t71359723
Null Geodesics in Five Dimensional Manifolds
We analyze a class of 5D non-compact warped-product spaces characterized by
metrics that depend on the extra coordinate via a conformal factor. Our model
is closely related to the so-called canonical coordinate gauge of Mashhoon et
al. We confirm that if the 5D manifold in our model is Ricci-flat, then there
is an induced cosmological constant in the 4D sub-manifold. We derive the
general form of the 5D Killing vectors and relate them to the 4D Killing
vectors of the embedded spacetime. We then study the 5D null geodesic paths and
show that the 4D part of the motion can be timelike -- that is, massless
particles in 5D can be massive in 4D. We find that if the null trajectories are
affinely parameterized in 5D, then the particle is subject to an anomalous
acceleration or fifth force. However, this force may be removed by
reparameterization, which brings the correct definition of the proper time into
question. Physical properties of the geodesics -- such as rest mass variations
induced by a variable cosmological ``constant'', constants of the motion and 5D
time-dilation effects -- are discussed and are shown to be open to experimental
or observational investigation.Comment: 19 pages, REVTeX, in press in Gen. Rel. Gra
Superdiffusivity of Asymmetric Energy Model in Dimension One and Two
We discuss an asymmetric energy model (AEM) introduced by Giardina et al. in
\cite{7}. This model is expected to belong to the KPZ class. We obtain lower
bounds for the diffusion coefficient. In particular, the diffusion coefficient
is diverging in dimension one and two as it is expected in the KPZ picture
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