6,032 research outputs found
A Renewal version of the Sanov theorem
Large deviations for the local time of a process are investigated,
where for and are i.i.d.\ random
variables on a Polish space, is the -th arrival time of a renewal
process depending on . No moment conditions are assumed on the arrival
times of the renewal process.Comment: 13 page
An Algebraic Approach to Hough Transforms
The main purpose of this paper is to lay the foundations of a general theory
which encompasses the features of the classical Hough transform and extend them
to general algebraic objects such as affine schemes. The main motivation comes
from problems of detection of special shapes in medical and astronomical
images. The classical Hough transform has been used mainly to detect simple
curves such as lines and circles. We generalize this notion using reduced
Groebner bases of flat families of affine schemes. To this end we introduce and
develop the theory of Hough regularity. The theory is highly effective and we
give some examples computed with CoCoA
Large deviations for a random speed particle
We investigate large deviations for the empirical measure of the position and
momentum of a particle traveling in a box with hot walls. The particle travels
with uniform speed from left to right, until it hits the right boundary. Then
it is absorbed and re-emitted from the left boundary with a new random speed,
taken from an i.i.d. sequence. It turns out that this simple model, often used
to simulate a heat bath, displays unusually complex large deviations features,
that we explain in detail. In particular, if the tail of the update
distribution of the speed is sufficiently oscillating, then the empirical
measure does not satisfy a large deviations principle, and we exhibit optimal
lower and upper large deviations functionals
The role of environmental correlations in the non-Markovian dynamics of a spin system
We put forward a framework to study the dynamics of a chain of interacting
quantum particles affected by individual or collective multi-mode environment,
focussing on the role played by the environmental quantum correlations over the
evolution of the chain. The presence of entanglement in the state of the
environmental system magnifies the non-Markovian nature of the chain's
dynamics, giving rise to structures in figures of merit such as entanglement
and purity that are not observed under a separable multi-mode environment. Our
analysis can be relevant to problems tackling the open-system dynamics of
biological complexes of strong current interest.Comment: 9 pages, 12 figure
The relative energy of homogeneous and isotropic universes from variational principles
We calculate the relative conserved currents, superpotentials and conserved
quantities between two homogeneous and isotropic universes. In particular we
prove that their relative "energy" (defined as the conserved quantity
associated to cosmic time coordinate translations for a comoving observer) is
vanishing and so are the other conserved quantities related to a Lie subalgebra
of vector fields isomorphic to the Poincar\'e algebra. These quantities are
also conserved in time. We also find a relative conserved quantity for such a
kind of solutions which is conserved in time though non-vanishing. This example
provides at least two insights in the theory of conserved quantities in General
Relativity. First, the contribution of the cosmological matter fluid to the
conserved quantities is carefully studied and proved to be vanishing. Second,
we explicitly show that our superpotential (that happens to coincide with the
so-called KBL potential although it is generated differently) provides strong
conservation laws under much weaker hypotheses than the ones usually required.
In particular, the symmetry generator is not needed to be Killing (nor Killing
of the background, nor asymptotically Killing), the prescription is quasi-local
and it works fine in a finite region too and no matching condition on the
boundary is required.Comment: Corrected typos and improved forma
Chetaev vs. vakonomic prescriptions in constrained field theories with parametrized variational calculus
Starting from a characterization of admissible Cheataev and vakonomic
variations in a field theory with constraints we show how the so called
parametrized variational calculus can help to derive the vakonomic and the
non-holonomic field equations. We present an example in field theory where the
non-holonomic method proved to be unphysical
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