Xuan Wu
University of Illinois Urbana-Champaign, IL·Mathematics & Statistics
When a surface grows through random deposits, its edge forms a rough, fluctuating interface. Examples include a burning sheet of paper, a bacterial colony or a growing crystal.
- Fields
Mathematics & Statistics
Physics
- Topics
KPZ equation
Kardar-Parisi-Zhang
KPZ universality class
- Grants
- 1 known grant, through Jul 2027
What they work on
- 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.
- Prove that the Airy line ensemble arises as a universal limit under broader and milder assumptions than the exactly solvable models where it is currently known to appear.
- Use Gibbsian line ensembles, building on the Bessel line ensemble, to study the Laguerre unitary ensemble, a random matrix model outside the KPZ universality class.
More about the research
The Kardar-Parisi-Zhang (KPZ) equation, introduced in 1986, became physicists' default model for this kind of random interface growth. Many seemingly different random systems share the same large-scale statistics, and together they are called the KPZ universality class. This project studies the KPZ equation and related random processes using the Gibbs property. This is an internal consistency rule: any piece of the system, given its surroundings, behaves like a simple constrained random object. The goals are to help construct solutions to the KPZ equation and to understand its long-range correlations.
Why it matters
This is pure mathematics. It aims to deepen understanding of random growth processes and random matrices by placing them in a common framework built on the Gibbs property. Clearer results on the KPZ universality class could eventually inform the mathematical description of physical interface growth, which the KPZ equation was introduced to model.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Le Chen
Auburn University, AL·Mathematics & Statistics·Early-career
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.
Jacopo Borga
Massachusetts Institute of Technology, MA·Mathematics & Statistics
Link the longest increasing subsequence of random permutations to directed distances on random planar maps, aiming to build a 'quantum version' of the Kardar-Parisi-Zhang directed landscape.
Amir Dembo
Stanford University, CA·Mathematics & Statistics
Characterize the limiting behavior of large sparse random graphs, such as Erdős–Rényi graphs, through explicit variational formulas that do not depend on model details.
The school
University of Illinois Urbana-Champaign: 41 labs on PI Pages, $907M a year on research, 870 research doctorates a year.
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