7,260 research outputs found
Central limit theorems for Poisson hyperplane tessellations
We derive a central limit theorem for the number of vertices of convex
polytopes induced by stationary Poisson hyperplane processes in .
This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab.
30 (1998) 640--656] for intersection points of motion-invariant Poisson line
processes in . Our proof is based on Hoeffding's decomposition of
-statistics which seems to be more efficient and adequate to tackle the
higher-dimensional case than the ``method of moments'' used in [Adv. in Appl.
Probab. 30 (1998) 640--656] to treat the case . Moreover, we extend our
central limit theorem in several directions. First we consider -flat
processes induced by Poisson hyperplane processes in for . Second we derive (asymptotic) confidence intervals for the
intensities of these -flat processes and, third, we prove multivariate
central limit theorems for the -dimensional joint vectors of numbers of
-flats and their -volumes, respectively, in an increasing spherical
region.Comment: Published at http://dx.doi.org/10.1214/105051606000000033 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Limit theorems for functionals on the facets of stationary random tessellations
We observe stationary random tessellations in
through a convex sampling window that expands unboundedly
and we determine the total -volume of those -dimensional manifold
processes which are induced on the -facets of () by their
intersections with the -facets of independent and identically
distributed motion-invariant tessellations generated within each cell
of . The cases of being either a Poisson hyperplane tessellation
or a random tessellation with weak dependences are treated separately. In both
cases, however, we obtain that all of the total volumes measured in are
approximately normally distributed when is sufficiently large. Structural
formulae for mean values and asymptotic variances are derived and explicit
numerical values are given for planar Poisson--Voronoi tessellations (PVTs) and
Poisson line tessellations (PLTs).Comment: Published at http://dx.doi.org/10.3150/07-BEJ6131 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Lepton number violation in theories with a large number of Standard Model copies
We examine lepton number violation (LNV) in theories with a saturated black
hole bound on a large number of species. Such theories have been advocated
recently as a possible solution to the hierarchy problem and an explanation of
the smallness of neutrino masses. The violation of lepton number can be a
potential phenomenological problem of this N-copy extension of the Standard
Model as due to the low quantum gravity scale black holes may induce TeV scale
LNV operators generating unacceptably large rates of LNV processes. We show,
however, that this does not happen in this scenario due to a specific
compensation mechanism between contributions of different Majorana neutrino
states to these processes. As a result rates of LNV processes are extremely
small and far beyond experimental reach, at least for the left-handed neutrino
states.Comment: 5 pages, 3 figure
Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks
We consider spatially homogeneous marked point patterns in an unboundedly
expanding convex sampling window. Our main objective is to identify the
distribution of the typical mark by constructing an asymptotic
-goodness-of-fit test. The corresponding test statistic is based on a
natural empirical version of the Palm mark distribution and a smoothed
covariance estimator which turns out to be mean square consistent. Our approach
does not require independent marks and allows dependences between the mark
field and the point pattern. Instead we impose a suitable -mixing
condition on the underlying stationary marked point process which can be
checked for a number of Poisson-based models and, in particular, in the case of
geostatistical marking. In order to study test performance, our test approach
is applied to detect anisotropy of specific Boolean models.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ523 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm). arXiv admin
note: substantial text overlap with arXiv:1205.504
Lepton number, black hole entropy and 10 to the 32 copies of the Standard Model
Lepton number violating processes are a typical problem in theories with a
low quantum gravity scale. In this paper we examine lepton number violation
(LNV) in theories with a saturated black hole bound on a large number of
species. Such theories have been advocated recently as a possible solution to
the hierarchy problem and an explanation of the smallness of neutrino masses.
Naively one would expect black holes to introduce TeV scale LNV operators, thus
generating unacceptably large rates of LNV processes. We show, however, that
this does not happen in this scenario due to a complicated compensation
mechanism between contributions of different Majorana neutrino states to these
processes. As a result rates of LNV processes are extremely small and far
beyond experimental reach, at least for the left-handed neutrino states.Comment: 6 pages, 3 figures, to appear in Proc. PASCOS 2010, Valencia, Spai
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