Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes

Alexei Borodin; Ivan Corwin; Patrik L. Ferrari

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arXiv · 1612.00321

Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes

Alexei Borodin·Ivan Corwin·Patrik L. Ferrari

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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 to 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.

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BibTeX RIS

Alexei Borodin, Ivan Corwin, Patrik L. Ferrari. 2016-12-01. Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes. https://arxiv.org/abs/1612.00321

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