Yao Li

Courant Instructor

Courant Institute of Mathematical Sciences,

New York University

My primary research areas are dynamical systems and stochastic processes. 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 existence of local thermodynamic equilibrium.


Related papers:

Polynomial Convergence to Equilibrium for a System of Interacing Particles (with Lai-Sang Young), Preprint

Local Thermodynamic Equilibrium for some Multidimensional Stochastic Models (with Peter Nandori and Lai-Sang Young) , Preprint (pdf)

On the stochastic modification of locally confined particle systems, Under Review (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), Under Review (pdf)

Systematic measures of biological networks, part II: Degeneracy, complexity and robustness. (with Yingfei Yi), Under Review (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)

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)

Numerical Analysis

A limiting strategy for the back and forth error compensation and correction method for solving advection equations (with L. Hu, Y. Liu), Under Review (pdf)