1,835 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
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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