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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 |
Description
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.