167 research outputs found
Martin boundary of a reflected random walk on a half-space
The complete representation of the Martin compactification for reflected
random walks on a half-space is obtained. It is shown that the
full Martin compactification is in general not homeomorphic to the ``radial''
compactification obtained by Ney and Spitzer for the homogeneous random walks
in : convergence of a sequence of points to a
point of on the Martin boundary does not imply convergence of the sequence
on the unit sphere . Our approach relies on the large
deviation properties of the scaled processes and uses Pascal's method combined
with the ratio limit theorem. The existence of non-radial limits is related to
non-linear optimal large deviation trajectories.Comment: 42 pages, preprint, CNRS UMR 808
Survival, extinction and approximation of discrete-time branching random walks
We consider a general discrete-time branching random walk on a countable set
X. We relate local, strong local and global survival with suitable inequalities
involving the first-moment matrix M of the process. In particular we prove
that, while the local behavior is characterized by M, the global behavior
cannot be completely described in terms of properties involving M alone.
Moreover we show that locally surviving branching random walks can be
approximated by sequences of spatially confined and stochastically dominated
branching random walks which eventually survive locally if the (possibly
finite) state space is large enough. An analogous result can be achieved by
approximating a branching random walk by a sequence of multitype contact
processes and allowing a sufficiently large number of particles per site. We
compare these results with the ones obtained in the continuous-time case and we
give some examples and counterexamples.Comment: 32 pages, a few misprints have been correcte
Orbital parameters, masses and distance to Beta Centauri determined with the Sydney University Stellar Interferometer and high resolution spectroscopy
The bright southern binary star beta Centauri (HR 5267) has been observed
with the Sydney University Stellar Interferometer (SUSI) and spectroscopically
with the ESO CAT and Swiss Euler telescopes at La Silla. The interferometric
observations have confirmed the binary nature of the primary component and have
enabled the determination of the orbital parameters of the system. At the
observing wavelength of 442 nm the two components of the binary system have a
magnitude difference of 0.15. The combination of interferometric and
spectroscopic data gives the following results: orbital period 357 days,
semi-major axis 25.30 mas, inclination 67.4 degrees, eccentricity 0.821,
distance 102.3 pc, primary and secondary masses M1 = M2 = 9.1 solar masses and
absolute visual magnitudes of the primary and secondary M1V = -3.85 and M2V =
-3.70. The high accuracy of the results offers a fruitful starting point for
future asteroseismic modelling of the pulsating binary components.Comment: 10 pages, 4 figures. Accepted for publication in MNRA
Boundaries of Disk-like Self-affine Tiles
Let be a disk-like self-affine tile generated by an
integral expanding matrix and a consecutive collinear digit set , and let be the characteristic polynomial of . In the
paper, we identify the boundary with a sofic system by
constructing a neighbor graph and derive equivalent conditions for the pair
to be a number system. Moreover, by using the graph-directed
construction and a device of pseudo-norm , we find the generalized
Hausdorff dimension where
is the spectral radius of certain contact matrix . Especially,
when is a similarity, we obtain the standard Hausdorff dimension where is the largest positive zero of
the cubic polynomial , which is simpler than
the known result.Comment: 26 pages, 11 figure
Orbital elements, masses and distance of lambda Scorpii A and B determined with the Sydney University Stellar Interferometer and high resolution spectroscopy
The triple system HD158926 (lambda Sco) has been observed interferometrically
with the Sydney University Stellar Interferometer and the elements of the wide
orbit have been determined. These are significantly more accurate than the
previous elements found spectroscopically. The inclination of the wide orbit is
consistent with the inclination previously found for the orbit of the close
companion. The wide orbit also has low eccentricity, suggesting that the three
stars were formed at the same time.
The brightness ratio between the two B stars was also measured at lambda =
442nm and 700nm. The brightness ratio and colour index are consistent with the
previous classification of lambda Sco A as B1.5 and lambda Sco B as B2.
Evolutionary models show that the two stars lie on the main sequence. Since
they have have the same age and luminosity class (IV) the mass-luminosity
relation can be used to determine the mass ratio of the two stars: M_B/M_A =
0.76+/-0.04.
The spectroscopic data have been reanalyzed using the interferometric values
for P, T, e and omega, leading to revised values for a_1sin i and the mass
function. The individual masses can be found from the mass ratio, the mass
function, spectrum synthesis and the requirement that the age of both
components must be the same: M_A = 10.4+/-1.3 Msun and M_B = 8.1+/-1.0 Msun.
The masses, angular semimajor axis and the period of the system can be used
to determine the dynamical parallax. We find the distance to lambda Sco to be
112+/-5 pc, which is approximately a factor of two closer than the HIPPARCOS
value of 216+/-42 pc.Comment: 8 pages, 4 figures. Accepted for publication by Monthly Notices of
the Royal Astronomical Societ
Random tree growth by vertex splitting
We study a model of growing planar tree graphs where in each time step we
separate the tree into two components by splitting a vertex and then connect
the two pieces by inserting a new link between the daughter vertices. This
model generalises the preferential attachment model and Ford's -model
for phylogenetic trees. We develop a mean field theory for the vertex degree
distribution, prove that the mean field theory is exact in some special cases
and check that it agrees with numerical simulations in general. We calculate
various correlation functions and show that the intrinsic Hausdorff dimension
can vary from one to infinity, depending on the parameters of the model.Comment: 47 page
Nonequilibrium stationary states and equilibrium models with long range interactions
It was recently suggested by Blythe and Evans that a properly defined steady
state normalisation factor can be seen as a partition function of a fictitious
statistical ensemble in which the transition rates of the stochastic process
play the role of fugacities. In analogy with the Lee-Yang description of phase
transition of equilibrium systems, they studied the zeroes in the complex plane
of the normalisation factor in order to find phase transitions in
nonequilibrium steady states. We show that like for equilibrium systems, the
``densities'' associated to the rates are non-decreasing functions of the rates
and therefore one can obtain the location and nature of phase transitions
directly from the analytical properties of the ``densities''. We illustrate
this phenomenon for the asymmetric exclusion process. We actually show that its
normalisation factor coincides with an equilibrium partition function of a walk
model in which the ``densities'' have a simple physical interpretation.Comment: LaTeX, 23 pages, 3 EPS figure
Multi-agent Coordination in Directed Moving Neighborhood Random Networks
In this paper, we consider the consensus problem of dynamical multiple agents
that communicate via a directed moving neighborhood random network. Each agent
performs random walk on a weighted directed network. Agents interact with each
other through random unidirectional information flow when they coincide in the
underlying network at a given instant. For such a framework, we present
sufficient conditions for almost sure asymptotic consensus. Some existed
consensus schemes are shown to be reduced versions of the current model.Comment: 9 page
Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensemble
The paper studies the spectral properties of large Wigner, band and sample
covariance random matrices with heavy tails of the marginal distributions of
matrix entries.Comment: This is an extended version of my talk at the QMath 9 conference at
Giens, France on September 13-17, 200
On the order of summability of the Fourier inversion formula
In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems
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