Stochastic Heat Equation Limit of a (2 + 1)d Growth Model
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1601.02767.pdf
Description
Submitted version
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546.6 KB
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Author(s)
Borodin, Alexei
Corwin, Ivan
Toninelli, Fabio Lucio
Date Issued
2017
Journal
Communications in Mathematical Physics
Publisher
Springer Nature
Citation
Borodin, Alexei, Ivan Corwin, and Fabio Lucio Toninelli. "Stochastic Heat Equation Limit of a (2+1)D Growth Model." Communications in Mathematical Physics 350 3 (2017): 957-84.
Version
Original manuscript
Abstract
© 2016, Springer-Verlag Berlin Heidelberg. We determine a q→ 1 limit of the two-dimensional q-Whittaker driven particle system on the torus studied previously in Corwin and Toninelli (Electron. Commun. Probab. 21(44):1–12, 2016). This has an interpretation as a (2 + 1)-dimensional stochastic interface growth model, which is believed to belong to the so-called anisotropic Kardar–Parisi–Zhang (KPZ) class. This limit falls into a general class of two-dimensional systems of driven linear SDEs which have stationary measures on gradients. Taking the number of particles to infinity we demonstrate Gaussian free field type fluctuations for the stationary measure. Considering the temporal evolution of the stationary measure, we determine that along characteristics, correlations are asymptotically given by those of the (2 + 1)-dimensional additive stochastic heat equation. This confirms (for this model) the prediction that the non-linearity for the anisotropic KPZ equation in (2 + 1)-dimension is irrelevant.
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/S00220-016-2718-4
