2,078 research outputs found
Large Deviations Principle for Stochastic Scalar Conservation Laws
We investigate large deviations for a family of conservative stochastic PDEs
(conservation laws) in the asymptotic of jointly vanishing noise and viscosity.
We obtain a first large deviations principle in a space of Young measures. The
associated rate functional vanishes on a wide set, the so-called set of
measure-valued solutions to the limiting conservation law. We therefore
investigate a second order large deviations principle, thus providing a
quantitative characterization of non-entropic solutions to the conservation
law.Comment: 40 page
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
Full metastable asymptotic of the Fisher information
We establish an expansion by Gamma-convergence of the Fisher information
relative to the reference measure exp(-beta V), where V is a generic multiwell
potential and beta goes to infinity. The expansion reveals a hierarchy of
multiple scales reflecting the metastable behavior of the underlying overdamped
Langevin dynamics: distinct scales emerge and become relevant depending on
whether one considers probability measures concentrated on local minima of V,
probability measures concentrated on critical points of V, or generic
probability measures on R^d. We thus fully describe the asymptotic behavior of
minima of the Fisher information over regular sets of probabilities. The
analysis mostly relies on spectral properties of diffusion operators and the
related semiclassical Witten Laplacian and covers also the case of a compact
smooth manifold as underlying space.Comment: 24 pages. Typos correcte
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
Quasi-potentials of the entropy functionals for scalar conservation laws
We investigate the quasi-potential problem for the entropy cost functionals
of non-entropic solutions to scalar conservation laws with smooth fluxes. We
prove that the quasi-potentials coincide with the integral of a suitable
Einstein entropy.Comment: 26 pages, 4 figure
Large deviations of the current in stochastic collisional dynamics
We consider a class of deterministic local collisional dynamics, showing how
to approximate them by means of stochastic models and then studying the
fluctuations of the current of energy. We show first that the variance of the
time-integrated current is finite and related to the conductivity by the
Green-Kubo relation. Next we show that the law of the empirical average current
satisfies a large deviations principle and compute explicitly the rate
functional in a suitable scaling limit. We observe that this functional is not
strictly convex.Comment: keywords and references adde
Some Remarks on Negation and Quantification in Leibniz’s Logic
We argue, with special reference to various passages
from Leibniz’s Generales Inquisitiones, that the simultaneous presence
of two switches concerning the negation operator is the main
source of the difficulties raised by many people against his logical
investigations. The former switch carries negation from outside to
inside of the proposition to which it is applied; the latter is the socalled
obversion law (which asserts the equivalence of “non est” and
“est non”). Applied in sequence, the two switches transform an outside
(propositional or de dicto) negation into a conceptual (predicative
or de re) negation. We also investigate the further difficulties
which arise from the interplay between these switches and Leibniz’s
use of indefinite letters
Convergence of the one-dimensional Cahn-Hilliard equation
We consider the Cahn-Hilliard equation in one space dimension with scaling a
small parameter \epsilon and a non-convex potential W. In the limit \espilon
\to 0, under the assumption that the initial data are energetically
well-prepared, we show the convergence to a Stefan problem. The proof is based
on variational methods and exploits the gradient flow structure of the
Cahn-Hilliard equation.Comment: 23 page
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