5,745 research outputs found
Critical random graphs: limiting constructions and distributional properties
We consider the Erdos-Renyi random graph G(n,p) inside the critical window,
where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous
paper (arXiv:0903.4730) that considering the connected components of G(n,p) as
a sequence of metric spaces with the graph distance rescaled by n^{-1/3} and
letting n go to infinity yields a non-trivial sequence of limit metric spaces C
= (C_1, C_2, ...). These limit metric spaces can be constructed from certain
random real trees with vertex-identifications. For a single such metric space,
we give here two equivalent constructions, both of which are in terms of more
standard probabilistic objects. The first is a global construction using
Dirichlet random variables and Aldous' Brownian continuum random tree. The
second is a recursive construction from an inhomogeneous Poisson point process
on R_+. These constructions allow us to characterize the distributions of the
masses and lengths in the constituent parts of a limit component when it is
decomposed according to its cycle structure. In particular, this strengthens
results of Luczak, Pittel and Wierman by providing precise distributional
convergence for the lengths of paths between kernel vertices and the length of
a shortest cycle, within any fixed limit component.Comment: 30 pages, 4 figure
Critical random graphs : limiting constructions and distributional properties
We consider the Erdos-Renyi random graph G(n, p) inside the critical window, where p = 1/n + lambda n(-4/3) for some lambda is an element of R. We proved in Addario-Berry et al. [2009+] that considering the connected components of G(n, p) as a sequence of metric spaces with the graph distance rescaled by n(-1/3) and letting n -> infinity yields a non-trivial sequence of limit metric spaces C = (C-1, C-2,...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak et al. [1994] by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component
Quantum Monte Carlo simulations of a particle in a random potential
In this paper we carry out Quantum Monte Carlo simulations of a quantum
particle in a one-dimensional random potential (plus a fixed harmonic
potential) at a finite temperature. This is the simplest model of an interface
in a disordered medium and may also pertain to an electron in a dirty metal. We
compare with previous analytical results, and also derive an expression for the
sample to sample fluctuations of the mean square displacement from the origin
which is a measure of the glassiness of the system. This quantity as well as
the mean square displacement of the particle are measured in the simulation.
The similarity to the quantum spin glass in a transverse field is noted. The
effect of quantum fluctuations on the glassy behavior is discussed.Comment: 23 pages, 7 figures included as eps files, uses RevTeX. Accepted for
publication in J. of Physics A: Mathematical and Genera
Large time dynamics and aging of a polymer chain in a random potential
We study the out-of-equilibrium large time dynamics of a gaussian polymer
chain in a quenched random potential. The dynamics studied is a simple Langevin
dynamics commonly referred to as the Rouse model. The equations for the
two-time correlation and response function are derived within the gaussian
variational approximation. In order to implement this approximation faithfully,
we employ the supersymmetric representation of the Martin-Siggia-Rose dynamical
action. For a short ranged correlated random potential the equations are solved
analytically in the limit of large times using certain assumptions concerning
the asymptotic behavior. Two possible dynamical behaviors are identified
depending upon the time separation- a stationary regime and an aging regime. In
the stationary regime time translation invariance holds and so is the
fluctuation dissipation theorem. The aging regime which occurs for large time
separations of the two-time correlation functions is characterized by history
dependence and the breakdown of certain equilibrium relations. The large time
limit of the equations yields equations among the order parameters that are
similar to the equations obtained in the statics using replicas. In particular
the aging solution corresponds to the broken replica solution. But there is a
difference in one equation that leads to important consequences for the
solution. The stationary regime corresponds to the motion of the polymer inside
a local minimum of the random potential, whereas in the aging regime the
polymer hops between different minima. As a byproduct we also solve exactly the
dynamics of a chain in a random potential with quadratic correlations.Comment: 21 pages, RevTeX
Logarithmic roughening in a growth process with edge evaporation
Roughening transitions are often characterized by unusual scaling properties.
As an example we investigate the roughening transition in a solid-on-solid
growth process with edge evaporation [Phys. Rev. Lett. 76, 2746 (1996)], where
the interface is known to roughen logarithmically with time. Performing
high-precision simulations we find appropriate scaling forms for various
quantities. Moreover we present a simple approximation explaining why the
interface roughens logarithmically.Comment: revtex, 6 pages, 7 eps figure
NICMOS Observations of Low-Redshift Quasar Host Galaxies
We have obtained Near-Infrared Camera and Multi-Object Spectrometer images of
16 radio quiet quasars observed as part of a project to investigate the
``luminosity/host-mass limit.'' The limit results were presented in McLeod,
Rieke, & Storrie-Lombardi (1999). In this paper, we present the images
themselves, along with 1- and 2-dimensional analyses of the host galaxy
properties. We find that our model-independent 1D technique is reliable for use
on ground-based data at low redshifts; that many radio-quiet quasars live in
deVaucouleurs-law hosts, although some of the techniques used to determine host
type are questionable; that complex structure is found in many of the hosts,
but that there are some hosts that are very smooth and symmetric; and that the
nuclei radiate at ~2-20% of the Eddington rate based on the assumption that all
galaxies have central black holes with a constant mass fraction of 0.6%.
Despite targeting hard-to-resolve hosts, we have failed to find any that imply
super-Eddington accretion rates.Comment: To appear in ApJ, 28 pages including degraded figures. Download the
paper with full-resolutio figures from
http://www.astro.wellesley.edu/kmcleod/mm.p
Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O in the presence of straight and of tilted columnar defects
In this paper we use London Langevin molecular dynamics simulations to
investigate the vortex matter melting transition in the highly anisotropic
high-temperature superconductor material Bi_2Sr_2CaCu_2O in the
presence of low concentration of columnar defects (CDs). We reproduce with
further details our previous results obtained by using Multilevel Monte Carlo
simulations that showed that the melting of the nanocrystalline vortex matter
occurs in two stages: a first stage melting into nanoliquid vortex matter and a
second stage delocalization transition into a homogeneous liquid. Furthermore,
we report on new dynamical measurements in the presence of a current that
identifies clearly the irreversibility line and the second stage delocalization
transition. In addition to CDs aligned along the c-axis we also simulate the
case of tilted CDs which are aligned at an angle with respect to the applied
magnetic field. Results for CDs tilted by with respect to c-axis
show that the locations of the melting and delocalization transitions are not
affected by the tilt when the ratio of flux lines to CDs remains constant. On
the other hand we argue that some dynamical properties and in particular the
position of the irreversibility line should be affected.Comment: 13 pages, 11 figure
A comparison of the optical properties of radio-loud and radio-quiet quasars
We have made radio observations of 87 optically selected quasars at 5 GHz
with the VLA in order to measure the radio power for these objects and hence
determine how the fraction of radio-loud quasars varies with redshift and
optical luminosity. The sample has been selected from the recently completed
Edinburgh Quasar Survey and covers a redshift range of 0.3 < z < 1.5 and an
optical absolute magnitude range of -26.5 < M_{B} < -23.5 (h, q_{0} = 1/2). We
have also matched up other existing surveys with the FIRST and NVSS radio
catalogues and combined these data so that the optical luminosity-redshift
plane is now far better sampled than previously. We have fitted a model to the
probability of a quasar being radio-loud as a function of absolute magnitude
and redshift and from this model infer the radio-loud and radio-quiet optical
luminosity functions. The radio-loud optical luminosity function is featureless
and flatter than the radio-quiet one. It evolves at a marginally slower rate if
quasars evolve by density evolution, but the difference in the rate of
evolutions of the two different classes is much less than was previously
thought. We show, using Monte-Carlo simulations, that the observed difference
in the shape of the optical luminosity functions can be partly accounted for by
Doppler boosting of the optical continuum of the radio-loud quasars and explain
how this can be tested in the future.Comment: 33 pages, 9 postscript figures, uses the AAS aaspp4 LaTeX style file,
to appear in the 1 February 1999 issue of The Astrophysical Journa
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