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How to solve the Kardar-Parisi-Zhang stochastic PDE
Probability| Speaker: | Ivan Corwin, Courant Institute |
| Location: | 3106 MSB |
| Start time: | Wed, Oct 20 2010, 4:10PM |
The Kardar-Parisi-Zhang (KPZ) stochastic PDE is the central object in the study of random growth models, interacting particle systems and random polymer models. Bertini and Giacomin provide an approach for defining and approximating this SPDE (properly interpreted) as the limit of an interacting particle system -- the weakly asymmetric exclusion process. Tracy and Widom provide certain exact transition formulas for this particle system. Combining these two approaches we are able to derive and prove the first exact formula for the distribution function for the solution to the KPZ equation. This talk is based on joint work with Gideon Amir and Jeremy Quastel.