Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes
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Author(s)
Corwin, Ivan
Ferrari, Patrik L.
Borodin, Alexei
Date Issued
October 2017
Journal
Probability Theory and Related Fields
Publisher
Springer Berlin Heidelberg
Citation
Borodin, Alexei, et al. “Anisotropic (2+1)d Growth and Gaussian Limits of q-Whittaker Processes.” Probability Theory and Related Fields, vol. 172, no. 1–2, Oct. 2018, pp. 245–321.
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Author's final manuscript
Abstract
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
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00440-017-0809-6
