21,295 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
Inflated Beta Distributions
This paper considers the issue of modeling fractional data observed in the
interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are
proposed. The beta distribution is used to describe the continuous component of
the model since its density can have quite diferent shapes depending on the
values of the two parameters that index the distribution. Properties of the
proposed distributions are examined. Also, maximum likelihood and method of
moments estimation is discussed. Finally, practical applications that employ
real data are presented.Comment: 15 pages, 4 figures. Submitted to Statistical Paper
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
Local power of the LR, Wald, score and gradient tests in dispersion models
We derive asymptotic expansions up to order for the nonnull
distribution functions of the likelihood ratio, Wald, score and gradient test
statistics in the class of dispersion models, under a sequence of Pitman
alternatives. The asymptotic distributions of these statistics are obtained for
testing a subset of regression parameters and for testing the precision
parameter. Based on these nonnull asymptotic expansions it is shown that there
is no uniform superiority of one test with respect to the others for testing a
subset of regression parameters. Furthermore, in order to compare the
finite-sample performance of these tests in this class of models, Monte Carlo
simulations are presented. An empirical application to a real data set is
considered for illustrative purposes.Comment: Submitted for publicatio
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
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.
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