Le Chen
Auburn University, AL·Mathematics & Statistics·Early-career
Many natural and industrial processes evolve in time while being constantly jostled by randomness: a tumor expanding, a fire front spreading through a forest, sediment moving in a river, a growing crystal surface. Stochastic partial differential equations (SPDEs) are the mathematical objects used to describe such systems, combining a deterministic evolution rule with random noise.
- Fields
Mathematics & Statistics
Physics
- Topics
stochastic partial differential equations
stochastic heat equation
parabolic Anderson model
- Grants
- 1 known grant, through Jun 2030
What they work on
- Prove the existence of nontrivial invariant measures for the stochastic heat equation and the parabolic Anderson model, arising from the interaction between noise structure and rough initial data.
- Resolve open problems on moment estimates of the Malliavin derivative, a stochastic-calculus tool for differentiating random quantities, in order to extend the reach of Malliavin calculus for SPDEs.
- Develop a unified theoretical framework through fractional stochastic PDEs that interpolates among known properties, including sample path regularity of the stochastic heat equation and the stochastic wave equation.
- Study the Kardar-Parisi-Zhang equation, a model of randomly growing interfaces, under rough initial data and diverse noise structures, and run simulations with inhomogeneous particles and long-range correlations to generate new conjectures about disordered systems.
More about the research
Analyzing them is hard, especially when the starting configuration is irregular or the noise has unusual structure, and this project attacks several of the resulting open problems.
Why it matters
The equations studied here are the working models for randomly driven growth and spreading, so sharper results on their long-run behavior and regularity feed into how scientists model tumor growth, fire propagation, sediment transport, and surface formation in pharmaceutical and semiconductor manufacturing. The techniques are also intended to connect with finance, numerical analysis, engineering, and machine learning.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Sandra Cerrai
University of Maryland, MD·Mathematics & Statistics
Prove that the Smoluchowski-Kramers small-mass limit holds for stochastic damped geometric wave equations, starting with one-dimensional stochastic wave maps.
Xuan Wu
University of Illinois Urbana-Champaign, IL·Mathematics & Statistics
Establish connections between the KPZ equation, a model of random interface growth, and the KPZ line ensemble, a family of interacting random curves, using their shared Gibbs properties.
Bjoern Bringmann
Princeton University, NJ·Mathematics & Statistics
Prove that the Gibbs measure of the three-dimensional cubic nonlinear Schrödinger equation is invariant under its dynamics. This would be the first invariance result for a Gibbs measure that is critical with respect to probabilistic scaling.
The school
Auburn University: 11 labs on PI Pages, $394M a year on research, 327 research doctorates a year.
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