BIRS Workshop Lecture Videos
Lower-tail of the KPZ equation via Coulomb gas Tsai, Li-Cheng
We establish a Large Deviation Principle (LDP) for the lower-tail of the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial condition. Our analysis exploits an exact connection between the KPZ one-point distribution and the Airy Point Process (PP). The latter is a semi-infinite particle system arises at the spectral edge the Gaussian Unitary Ensemble. We develop the LDP for the Airy PP, with an explicitly rate function written in terms of electrostatic energy. From this rate function, we solve a variational problem to obtain the exact lower-tail LD rate function of the KPZ equation.
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