(2 + 1)-DIMENSIONAL INTERFACE DYNAMICS: MIXING TIME, HYDRODYNAMIC LIMIT AND ANISOTROPIC KPZ GROWTH

DOI10.1142/9789813272880_0158zbMath1453.82046arXiv1711.05571OpenAlexW2972670050MaRDI QIDQ5122133

Fabio Lucio Toninelli

Publication date: 22 September 2020

Published in: Proceedings of the International Congress of Mathematicians (ICM 2018) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.05571

zbMATH Keywords

stochastic heat equationhydrodynamic limitinteracting particle systemsdimer modelinterface growthanisotropic KPZ equation

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Heat equation (35K05) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) PDEs with randomness, stochastic partial differential equations (35R60) Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics (82C24) PDEs in connection with statistical mechanics (35Q82)

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Rescaled Whittaker driven stochastic differential equations converge to the additive stochastic heat equation ⋮ Fluctuations of the solutions to the KPZ equation in dimensions three and higher ⋮ The stationary AKPZ equation: Logarithmic superdiffusivity ⋮ Superconcentration in surface growth ⋮ Cutoff for the Glauber dynamics of the lattice free field ⋮ A $(2+1)$-dimensional anisotropic KPZ growth model with a smooth phase ⋮ The domino shuffling algorithm and anisotropic KPZ stochastic growth ⋮ Convergences of the rescaled Whittaker stochastic differential equations and independent sums ⋮ Hydrodynamic limit for a 2D interlaced particle process

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