13,745 research outputs found
Improved exponential stability for near-integrable quasi-convex Hamiltonians
In this article, we improve previous results on exponential stability for
analytic and Gevrey perturbations of quasi-convex integrable Hamiltonian
systems. In particular, this provides a sharper upper bound on the speed of
Arnold diffusion which we believe to be optimal
Remarks on step cocycles over rotations, centralizers and coboundaries
By using a cocycle generated by the step function over an irrational rotation , we present examples which illustrate different aspects
of the general theory of cylinder maps. In particular, we construct non ergodic
cocycles with ergodic compact quotients, cocycles generating an extension
with a small centralizer. The constructions are related
to diophantine properties of
A tightness criterion for random fields, with application to the Ising model
We present a criterion for a family of random distributions to be tight in
local H\"older and Besov spaces of possibly negative regularity. We then apply
this criterion to the magnetization field of the two-dimensional Ising model at
criticality, answering a question of Camia, Garban and Newman.Comment: 28 pages. EJP versio
Nodal solutions for the Choquard equation
We consider the general Choquard equations where is a
Riesz potential. We construct minimal action odd solutions for and minimal action nodal solutions for
. We introduce a new minimax principle for
least action nodal solutions and we develop new concentration-compactness
lemmas for sign-changing Palais--Smale sequences. The nonlinear Schr\"odinger
equation, which is the nonlocal counterpart of the Choquard equation, does not
have such solutions.Comment: 23 pages, revised version with additional details and symmetry
properties of odd solution
Backward stochastic differential equation driven by a marked point process: An elementary approach with an application to optimal control
We address a class of backward stochastic differential equations on a bounded
interval, where the driving noise is a marked, or multivariate, point process.
Assuming that the jump times are totally inaccessible and a technical condition
holds (see Assumption (A) below), we prove existence and uniqueness results
under Lipschitz conditions on the coefficients. Some counter-examples show that
our assumptions are indeed needed. We use a novel approach that allows
reduction to a (finite or infinite) system of deterministic differential
equations, thus avoiding the use of martingale representation theorems and
allowing potential use of standard numerical methods. Finally, we apply the
main results to solve an optimal control problem for a marked point process,
formulated in a classical way.Comment: Published at http://dx.doi.org/10.1214/15-AAP1132 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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