Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes
Abstract We consider a discrete model for anisotropic (2 + 1)-dimensional growth of an interface height function. Owing to a connection with q-Whittaker functions, this system enjoys many explicit integral formulas. By considering certain Gaussian stochastic differential equation limits of the model...
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| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg,
2018-10-18T17:00:04Z.
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| Online Access: | Get fulltext |
| Summary: | Abstract We consider a discrete model for anisotropic (2 + 1)-dimensional growth of an interface height function. Owing to a connection with q-Whittaker functions, this system enjoys many explicit integral formulas. By considering certain Gaussian stochastic differential equation limits of the model we are able to prove a space-time limit of covariances to those of the (2 + 1)-dimensional additive stochastic heat equation (or Edwards-Wilkinson equation) along characteristic directions. In particular, the bulk height function converges to the Gaussian free field which evolves according to this stochastic PDE. Keywords: 2+1 growth models, KPZ universality class, q-Whittaker processes, Gaussian Free Field, Space-time process Galileo Galilei Institute for Theoretical Physics (Arcetri, Italy) Kavli Institute for Theoretical Physics National Science Foundation (U.S.) (Grant PHY-1125915) National Science Foundation (U.S.) (Grant DMS-1056390) National Science Foundation (U.S.) (Grant DMS-1607901) Simons Foundation. Postdoctoral Fellowship Radcliffe Institute for Advanced Study (Fellowship) |
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