My primary research areas are applied dynamical systems and applied probability. I work with random perturbed dynamical systems, and stochastic processes with a dynamical systems flavor, using both analytical and computational methods.

Nonequilibrium Statistical Mechanics

I am interested in a variety of problems arising from nonequilibrium statistical mechanics, such as the existence and uniqueness of nonequilibrium steady-states (NESS), exponential/polynomial convergence towards steady-states, and the microscopic derivation of thermodynamic laws. I am also interested in "nonequilibrium" neural field models.

Related papers:

- How well do reduced models capture the dynamics in models of interacting neurons? (with Logan Chariker and Lai-Sang Young),
*Under review*(pdf) - On the polynomial convergence rate to nonequilibrium steady-states,
*Under review*(pdf) - Polynomial Convergence to Equilibrium for a System of Interacing Particles (with Lai-Sang Young),
*Annals of Applied Probability, 27(1), 2017, 65-90*(pdf) - Local Thermodynamic Equilibrium for some Multidimensional Stochastic Models (with Peter Nandori and Lai-Sang Young) ,
*Journal of Statistical Physics, 163(1), 61-91*(pdf) - On the stochastic behaviors of locally confined particle systems,
*Chaos: An Interdisciplinary Journal of Nonlinear Science 25, 073121(2015)*(pdf) - Nonequilibrium steady states for a class of particle systems (with Lai-Sang Young),
*Nonlinearity 27, page 607, 2014*(pdf) - Existence of nonequilibrium steady state for a simple model of heat conduction (with Lai-Sang Young),
*Journal of Statistical Physics, pages 1 -- 24, 2013*(pdf)

Stochastic Differential Equations and Systematic Measures of Complex Networks

I am interested in invariant probability measures of stochastic differential equations. We obtained some new estimates of invariant probability measures of stochastic differential equations and applied them to complex biological networks. A class of systematic measures of biological network proposed in the literature of system biology, including degeneracy, complexity and robustness, are rigorously investigated and quantified.

Related papers:

- Systematic measures of biological networks, part I: Invariant measures and entropy (with Yingfei Yi),
*Communications on Pure and Applied Mathematics, LXIX, 1777-1811. 2016*(pdf) - Systematic measures of biological networks, part II: Degeneracy, complexity and robustness. (with Yingfei Yi),
*Communications on Pure and Applied Mathematics, LXIX, 1952-1983, 2016*(pdf) - Quantification of degeneracy in bio- logical systems for characterization of functional interactions between modules (with G. Dwivedi, W. Huang, M. Kemp and Y. Yi),
*Journal of theoretical biology, 302:2938, 2012*(pdf)

Numerical Analysis

- Numerical Simulation of Polynomial-Speed Convergence Phenomenon (with H. Xu),
*Journal of Statistical Physics, 169(4), 2017*(pdf) - A fast exact simulation algorithm for a class of Markov jump processes (with L. Hu),
*Journal of Chemical Physics, 143(18), 2015*(pdf) - A limiting strategy for the back and forth error compensation and correction method for solving advection equations (with L. Hu, Y. Liu),
*Mathematics of Computation 85 (2016), 1263-1280*(pdf)

Other publications:

Fokker-Planck Equations on Discrete Spaces

- Fokker-Planck equations for a free energy functional or Markov process on a graph (with S-N. Chow, W. Huang and H-M. Zhou),
*Archive for Rational Mechanics and Analysis 203.3 (2012): 969-1008.*(pdf) - A free energy based mathematical study for molecular motors (with S-N. Chow, W. Huang and H-M. Zhou),
*Regular and Chaotic Dynamics 16.1-2 (2011): 117-127.*(pdf) - Convergence to global equilibrium for Fokker-Planck equations on a graph and talagrand-type inequalities (with R. Che, W. Huang and P. Tetali),
*Under Review*(pdf)