322 citations · 1.5k across the 67 of their papers we have counts for
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(2+1)-dimensional interface dynamics: mixing time, hydrodynamic limit and Anisotropic KPZ growth
F. L. Toninelli
Stochastic interface dynamics serve as mathematical models for diverse time-dependent physical phenomena: the evolution of boundaries between thermodynamic phases, crystal growth,…
Speed and fluctuations for some driven dimer models
Sunil Chhita, Patrik L. Ferrari, Fabio Lucio Toninelli
We consider driven dimer models on the square and honeycomb graphs, starting from a stationary Gibbs measure. Each model can be thought of as a two dimensional stochastic growth mo…
Hydrodynamic limit and viscosity solutions for a 2D growth process in the anisotropic KPZ class
Martin Legras, Fabio Lucio Toninelli
We study a -dimensional stochastic interface growth model, that is believed to belong to the so-called Anisotropic KPZ (AKPZ) universality class [Borodin and Ferrari, 2014].…
Entropic repulsion in surfaces: a large deviation bound for all
Pietro Caputo, Fabio Martinelli, Fabio Lucio Toninelli
We consider the -dimensional generalized solid-on-solid (SOS) model, that is the random discrete surface with a gradient potential of the form , where $p\in […
Lozenge tiling dynamics and convergence to the hydrodynamic equation
Benoit Laslier, Fabio Lucio Toninelli
We study a reversible continuous-time Markov dynamics of a discrete -dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the $L\times…