77,570 research outputs found
Equivalence of weak and strong modes of measures on topological vector spaces
A strong mode of a probability measure on a normed space can be defined
as a point such that the mass of the ball centred at uniformly
dominates the mass of all other balls in the small-radius limit. Helin and
Burger weakened this definition by considering only pairwise comparisons with
balls whose centres differ by vectors in a dense, proper linear subspace of
, and posed the question of when these two types of modes coincide. We show
that, in a more general setting of metrisable vector spaces equipped with
measures that are finite on bounded sets, the density of and a uniformity
condition suffice for the equivalence of these two types of modes. We
accomplish this by introducing a new, intermediate type of mode. We also show
that these modes can be inequivalent if the uniformity condition fails. Our
results shed light on the relationships between among various notions of
maximum a posteriori estimator in non-parametric Bayesian inference.Comment: 22 pages, 3 figure
Quasi-invariance of countable products of Cauchy measures under non-unitary dilations
Consider an infinite sequence (Un)n∈N of independent Cauchy random variables, defined by a sequence (δn)n∈N of location parameters and a sequence (γn)n∈N of scale parameters. Let (Wn)n∈N be another infinite sequence of independent Cauchy random variables defined by the same sequence of location parameters and the sequence (σnγn)n∈N of scale parameters, with σn≠0 for all n∈N. Using a result of Kakutani on equivalence of countably infinite product measures, we show that the laws of (Un)n∈N and (Wn)n∈N are equivalent if and only if the sequence (|σn|−1)n∈N is square-summable
Sparticle Production in Electron-Photon Collisions
We explore the potential of electron-photon colliders to measure fundamental
supersymmetry parameters via the processes
(selectron-neutralino) and
(sneutrino-chargino). Given the and masses from
and hadron collider studies, cross section ratios
for opposite photon helicities determine
the , and masses, independent of the
sparticle branching fractions. The difference measures in a model-independent way. The
and masses test the universality of soft supersymmetry breaking
scalar masses. The cross section normalizations provide information about the
gaugino mixing parameters.Comment: add refs; add \tightenline
Supersymmetric QCD flavor changing top quark decay
We present a detailed and complete calculation of the gluino and scalar
quarks contribution to the flavour-changing top quark decay into a charm quark
and a photon, gluon, or a Z boson within the minimal supersymmetric standard
model including flavour changing gluino-quarks-scalar quarks couplings in the
right-handed sector. We compare the results with the ones presented in an
earlier paper where we considered flavour changing couplings only in the
left-handed sector. We show that these new couplings have important
consequences leading to a large enhancement when the mixing of the scalar
partners of the left- and right-handed top quark is included. Furthermore CP
violation in the flavour changing top quark decay will occur when a SUSY phase
is taken into account.Comment: 14 pages, latex, 3 figure
Commuting Simplicity and Closure Constraints for 4D Spin Foam Models
Spin Foam Models are supposed to be discretised path integrals for quantum
gravity constructed from the Plebanski-Holst action. The reason for there being
several models currently under consideration is that no consensus has been
reached for how to implement the simplicity constraints. Indeed, none of these
models strictly follows from the original path integral with commuting B
fields, rather, by some non standard manipulations one always ends up with non
commuting B fields and the simplicity constraints become in fact anomalous
which is the source for there being several inequivalent strategies to
circumvent the associated problems. In this article, we construct a new
Euclidian Spin Foam Model which is constructed by standard methods from the
Plebanski-Holst path integral with commuting B fields discretised on a 4D
simplicial complex. The resulting model differs from the current ones in
several aspects, one of them being that the closure constraint needs special
care. Only when dropping the closure constraint by hand and only in the large
spin limit can the vertex amplitudes of this model be related to those of the
FK Model but even then the face and edge amplitude differ. Curiously, an ad hoc
non-commutative deformation of the variables leads from our new model
to the Barrett-Crane Model in the case of Barbero-Immirzi parameter goes to
infinity.Comment: 41 pages, 4 figure
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