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Turbulent Liquid Crystals, KPZ Universality and the Asymmetric Simple Exclusion Process

Student-Run Applied & Math Seminar

Speaker: Craig Tracy, UC Davis
Location: 2112 MSB
Start time: Wed, May 25 2011, 12:10PM

We report on (1) recent experimental work on stochastically growing interfaces and (2) new theoretical developments for the KPZ equation, a stochastic nonlinear PDE, and the closely related asymmetric simple exclusion process. References: (1) K. Takeuchi andM. Sano, Universal fluctuations of growing interfaces: Evidence in turbulent liquid crystals, Phys. Rev. Let. 104, 230601 (2010). (2) G. Amir, I. Corwin and J. Quastel, Probability distribution of the free energy of the continuum directed random polymer in 1+1 dimensions, Commun. Pure and Applied Math. 64 (2011), 466–537. (3) T. Sasamoto and H. Spohn, One-dimensional Kardar-Parisi-Zhang equation: An exact solution and its universality, Phys. Rev. Let. 104, 230602 (2010). (4) C. A. Tracy and H. Widom, Integral formulas for the asymmetric simple exclusion process, Commun. Math. Phys. 279, 815–844 (2008), Erratum Commun. Math. Phys. 304, 875–878 (2011); Asymptotics in ASEP with step initial condition, Commun. Math. Phys. 290, 129–154 (2009); Total current fluctuations in the asymmetric simple exclusion process, J. Math. Phys. 50, 095204 (2009).