This $209,953 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support research on the Kardar-Parisi-Zhang (KPZ) equation and related stochastic processes at the University of Illinois. The project aims to leverage the "Gibbs property" of the KPZ equation to study its solution and understand long-range correlations. Key research directions include exploring the relation between the KPZ equation and KPZ line ensemble, establishing the universality of the Airy line ensemble, and using Gibbsian line ensembles to study the Laguerre unitary ensemble. The award will fund 3 years of research, student participation, workshops, and survey articles to advance the mathematical understanding of these stochastic processes and their applications. No sub-awards are planned under this grant.
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