Browsing by Subject "math.DS"
Now showing items 111 of 11

Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials
(20171130)We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the wellknown LennardJones type, and show that the system converges to the unique invariant Gibbs measure ... 
Geometric ergodicity of Langevin dynamics with Coulomb interactions
This paper is concerned with the long time behavior of Langevin dynamics of {\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order system of Brownian particles driven by an external force and ... 
Higher order asymptotics for large deviations  Part I
For sequences of nonlattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit ... 
Noiseinduced strong stabilization
We consider a 2dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes ... 
On the meanfield limit for the VlasovPoissonFokkerPlanck system
We devise and study a random particle blob method for approximating the VlasovPoissonFokkkerPlanck (VPFP) equations by a $N$particle system subject to the Brownian motion in $\mathbb{R}^3$ space. More precisely, we show ... 
Propagation of Fluctuations in Biochemical Systems, II: Nonlinear Chains
We consider biochemical reaction chains and investigate how random external fluctuations, as characterized by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption ... 
Scaling and Saturation in InfiniteDimensional Control Problems with Applications to Stochastic Partial Differential Equations
(20170727)We establish the dual notions of scaling and saturation from geometric control theory in an infinitedimensional setting. This generalization is applied to the lowmode control problem in a number of concrete nonlinear partial ... 
Scaling limits of a model for selection at two scales
The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. ... 
Scaling limits of a model for selection at two scales
(2015)The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. ... 
Singularities of invariant densities for random switching between two linear ODEs in 2D
We consider a planar dynamical system generated by two stable linear vector fields with distinct fixed points and random switching between them. We characterize singularities of the invariant density in terms of ... 
Smooth invariant densities for random switching on the torus
(20170830)We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2dtorus, with the random switchings happening according to a Poisson process. Assuming that the ...