187 research outputs found
Bounds for the variance of certain stationary point processes
AbstractFor the variance of stationary renewal and alternating renewal processes Nn(·) the paper establishes upper and lower bounds of the form −B1⩽varN8(0,x–Aλx⩽B2(0<x<∞), where λ=EN8(0,1), with constants A, B1 and B2 that depend on the first three moments of the interval distributions for the processes concerned. These results are consistent with the value of the constant A for a general stationary point process suggested by Cox in 1963 [1]
A stochastic epidemiological model and a deterministic limit for BitTorrent-like peer-to-peer file-sharing networks
In this paper, we propose a stochastic model for a file-sharing peer-to-peer
network which resembles the popular BitTorrent system: large files are split
into chunks and a peer can download or swap from another peer only one chunk at
a time. We prove that the fluid limits of a scaled Markov model of this system
are of the coagulation form, special cases of which are well-known
epidemiological (SIR) models. In addition, Lyapunov stability and settling-time
results are explored. We derive conditions under which the BitTorrent
incentives under consideration result in shorter mean file-acquisition times
for peers compared to client-server (single chunk) systems. Finally, a
diffusion approximation is given and some open questions are discussed.Comment: 25 pages, 6 figure
Emergence of influential spreaders in modified rumor models
The burst in the use of online social networks over the last decade has
provided evidence that current rumor spreading models miss some fundamental
ingredients in order to reproduce how information is disseminated. In
particular, recent literature has revealed that these models fail to reproduce
the fact that some nodes in a network have an influential role when it comes to
spread a piece of information. In this work, we introduce two mechanisms with
the aim of filling the gap between theoretical and experimental results. The
first model introduces the assumption that spreaders are not always active
whereas the second model considers the possibility that an ignorant is not
interested in spreading the rumor. In both cases, results from numerical
simulations show a higher adhesion to real data than classical rumor spreading
models. Our results shed some light on the mechanisms underlying the spreading
of information and ideas in large social systems and pave the way for more
realistic diffusion models.Comment: 14 Pages, 6 figures, accepted for publication in Journal of
Statistical Physic
The 5.2Â ka climate event: Evidence from stable isotope and multi-proxy palaeoecological peatland records in Ireland
AbstractEvidence for a major climate event at 5.2 ka has been reported globally and is associated with considerable societal disruption, but is poorly characterised in northwest Europe. This event forms part of a broader period of re-organisation in the Earth's ocean-atmosphere circulation system between 6 and 5 ka. This study tests the nature and timing of the event in northwest Europe, a region highly sensitive to change in meridional overturning circulation and mid-latitude westerly airflow. Here we report three high-resolution Irish multi-proxy records obtained from ombrotrophic peatlands that have robust chronological frameworks. We identify the 5.2 ka event by a sustained decrease in δ18Ocellulose at all three sites, with additional and parallel changes in δ13Ccellulose and palaeoecological (testate amoebae, plant macrofossil and humification) data from two sites in northern Ireland. Data from Sluggan Moss demonstrate a particularly coherent shift towards wetter conditions. These data support the hypothesis that the event was caused by a prolonged period of positive North Atlantic Oscillation conditions, resulting in pervasive cyclonic weather patterns across northwest Europe, increasing precipitation over Ireland
Countable Random Sets: Uniqueness in Law and Constructiveness
The first part of this article deals with theorems on uniqueness in law for
\sigma-finite and constructive countable random sets, which in contrast to the
usual assumptions may have points of accumulation. We discuss and compare two
approaches on uniqueness theorems: First, the study of generators for
\sigma-fields used in this context and, secondly, the analysis of hitting
functions. The last section of this paper deals with the notion of
constructiveness. We will prove a measurable selection theorem and a
decomposition theorem for constructive countable random sets, and study
constructive countable random sets with independent increments.Comment: Published in Journal of Theoretical Probability
(http://www.springerlink.com/content/0894-9840/). The final publication is
available at http://www.springerlink.co
Eynard-Mehta theorem, Schur process, and their pfaffian analogs
We give simple linear algebraic proofs of Eynard-Mehta theorem,
Okounkov-Reshetikhin formula for the correlation kernel of the Schur process,
and Pfaffian analogs of these results. We also discuss certain general
properties of the spaces of all determinantal and Pfaffian processes on a given
finite set.Comment: AMSTeX, 21 pages, a new section adde
Palm pairs and the general mass-transport principle
We consider a lcsc group G acting properly on a Borel space S and measurably
on an underlying sigma-finite measure space. Our first main result is a
transport formula connecting the Palm pairs of jointly stationary random
measures on S. A key (and new) technical result is a measurable disintegration
of the Haar measure on G along the orbits. The second main result is an
intrinsic characterization of the Palm pairs of a G-invariant random measure.
We then proceed with deriving a general version of the mass-transport principle
for possibly non-transitive and non-unimodular group operations first in a
deterministic and then in its full probabilistic form.Comment: 26 page
Edge scaling limits for a family of non-Hermitian random matrix ensembles
A family of random matrix ensembles interpolating between the GUE and the
Ginibre ensemble of matrices with iid centered complex Gaussian
entries is considered. The asymptotic spectral distribution in these models is
uniform in an ellipse in the complex plane, which collapses to an interval of
the real line as the degree of non-Hermiticity diminishes. Scaling limit
theorems are proven for the eigenvalue point process at the rightmost edge of
the spectrum, and it is shown that a non-trivial transition occurs between
Poisson and Airy point process statistics when the ratio of the axes of the
supporting ellipse is of order . In this regime, the family of
limiting probability distributions of the maximum of the real parts of the
eigenvalues interpolates between the Gumbel and Tracy-Widom distributions.Comment: 44 page
Translation-invariance of two-dimensional Gibbsian point processes
The conservation of translation as a symmetry in two-dimensional systems with
interaction is a classical subject of statistical mechanics. Here we establish
such a result for Gibbsian particle systems with two-body interaction, where
the interesting cases of singular, hard-core and discontinuous interaction are
included. We start with the special case of pure hard core repulsion in order
to show how to treat hard cores in general.Comment: 44 pages, 6 figure
R-local Delaunay inhibition model
Let us consider the local specification system of Gibbs point process with
inhib ition pairwise interaction acting on some Delaunay subgraph specifically
not con taining the edges of Delaunay triangles with circumscribed circle of
radius grea ter than some fixed positive real value . Even if we think that
there exists at least a stationary Gibbs state associated to such system, we do
not know yet how to prove it mainly due to some uncontrolled "negative"
contribution in the expression of the local energy needed to insert any number
of points in some large enough empty region of the space. This is solved by
introducing some subgraph, called the -local Delaunay graph, which is a
slight but tailored modification of the previous one. This kind of model does
not inherit the local stability property but satisfies s ome new extension
called -local stability. This weakened property combined with the local
property provides the existence o f Gibbs state.Comment: soumis \`{a} Journal of Statistical Physics 27 page
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