Now showing items 1-9 of 9

    • Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials 

      Herzog, David P; Mattingly, Jonathan Christopher (2017-11-30)
      We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure ...
    • Geometric ergodicity of Langevin dynamics with Coulomb interactions 

      Mattingly, Jonathan; Lu, Yulong
      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 

      Hebbar, Pratima; Fernando, Kasun
      For sequences of non-lattice 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 ...
    • On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system 

      Pickl, Peter; Huang, Hui; Liu, Jian-Guo
      We devise and study a random particle blob method for approximating the Vlasov-Poisson-Fokkker-Planck (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 

      Anderson, DF; Mattingly, Jonathan Christopher
      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 Infinite-Dimensional Control Problems with Applications to Stochastic Partial Differential Equations 

      Glatt-Holtz, NE; Herzog, David P; Mattingly, Jonathan Christopher (2017-07-27)
      We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial ...
    • Scaling limits of a model for selection at two scales 

      Luo, S; Mattingly, Jonathan Christopher
      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 

      Luo, S; Mattingly, Jonathan Christopher (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. ...
    • Smooth invariant densities for random switching on the torus 

      Bakhtin, Yuri; Hurth, T; Lawley, S; Mattingly, Jonathan Christopher (2017-08-30)
      We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the ...