322 citations · 1.5k across the 67 of their papers we have counts for
53 papers · 1 filter
Gaussian Fluctuations for the stochastic Burgers equation in dimension
Giuseppe Cannizzaro, Massimiliano Gubinelli, Fabio Toninelli
The goal of the present paper is to establish a framework which allows to rigorously determine the large-scale Gaussian fluctuations for a class of singular SPDEs at and above crit…
Kinetically constrained models out of equilibrium
Ivailo Hartarsky, Fabio Toninelli
We study the full class of kinetically constrained models in arbitrary dimension and out of equilibrium, in the regime where the density of facilitating sites in the equilibriu…
Non-reversible stationary states for majority voter and Ising dynamics on trees
Piet Lammers, Fabio Toninelli
We study three Markov processes on infinite, unrooted, regular trees: the stochastic Ising model (also known as the Glauber heat bath dynamics of the Ising model), a majority voter…
Height function localisation on trees
Piet Lammers, Fabio Toninelli
We study two models of discrete height functions, that is, models of random integer-valued functions on the vertices of a tree. First, we consider the random homomorphism model, in…
The mixing time of the lozenge tiling Glauber dynamics
Benoit Laslier, Fabio Toninelli
The broad motivation of this work is a rigorous understanding of reversible, local Markov dynamics of interfaces, and in particular their speed of convergence to equilibrium, measu…
Weakly non-planar dimers
Alessandro Giuliani, Bruno Renzi, Fabio Toninelli
We study a model of fully-packed dimer configurations (or perfect matchings) on a bipartite periodic graph that is two-dimensional but not planar. The graph is obtained from $\math…
Weak coupling limit of the Anisotropic KPZ equation
Giuseppe Cannizzaro, Dirk Erhard, Fabio Toninelli
In the present work, we study the two-dimensional anisotropic KPZ equation (AKPZ), which is formally given by \begin{equation*} \partial_t h=\tfrac12 Δh + λ((\partial_1 h)^2)-(\par…
-superdiffusivity for a Brownian particle in the curl of the 2d GFF
Giuseppe Cannizzaro, Levi Haunschmid-Sibitz, Fabio Toninelli
The present work is devoted to the study of the large time behaviour of a critical Brownian diffusion in two dimensions, whose drift is divergence-free, ergodic and given by the cu…
The stationary AKPZ equation: logarithmic superdiffusivity
Giuseppe Cannizzaro, Dirk Erhard, Fabio Toninelli
We study the two-dimensional Anisotropic KPZ equation (AKPZ) formally given by \begin{equation*} \partial_t H=\frac12ΔH+λ((\partial_1 H)^2-(\partial_2 H)^2)+ξ\,, \end{equation*} wh…
Hydrodynamic limit for a 2D interlaced particle process
Vincent Lerouvillois, Fabio Lucio Toninelli
The Markov dynamics of interlaced particle arrays, introduced by A. Borodin and P. Ferrari in arXiv:0811.0682, is a classical example of (2+1)-dimensional random growth model belon…
The domino shuffling algorithm and Anisotropic KPZ stochastic growth
Sunil Chhita, Fabio Lucio Toninelli
The domino-shuffling algorithm can be seen as a stochastic process describing the irreversible growth of a -dimensional discrete interface. Its stationary speed of growth $v…
Non-integrable dimer models: universality and scaling relations
Alessandro Giuliani, Fabio Lucio Toninelli
In the last few years, the methods of constructive Fermionic Renormalization Group have been successfully applied to the study of the scaling limit of several two-dimensional stati…
A (2+1)-dimensional Anisotropic KPZ growth model with a smooth phase
Sunil Chhita, Fabio Lucio Toninelli
Stochastic growth processes in dimension were conjectured by D. Wolf, on the basis of renormalization-group arguments, to fall into two distinct universality classes, accor…
(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…
Hydrodynamic limit equation for a lozenge tiling Glauber dynamics
B. Laslier, F. L. Toninelli
We study a reversible continuous-time Markov dynamics on lozenge tilings of the plane, introduced by Luby et al. Single updates consist in concatenations of elementary lozenge…
Stochastic heat equation limit of a (2+1)d growth model
Alexei Borodin, Ivan Corwin, Fabio Lucio Toninelli
We determine a limit of the two-dimensional -Whittaker driven particle system on the torus studied previously in [Corwin-Toninelli, arXiv:1509.01605]. This has an inter…
Stationary measure of the driven two-dimensional q-Whittaker particle system on the torus
Ivan Corwin, Fabio Lucio Toninelli
We consider a q-deformed version of the uniform Gibbs measure on dimers on the periodized hexagonal lattice (equivalently, on interlacing particle configurations, if vertical dimer…
Universality for the pinning model in the weak coupling regime
Francesco Caravenna, Fabio Lucio Toninelli, Niccolo Torri
We consider disordered pinning models, when the return time distribution of the underlying renewal process has a polynomial tail with exponent . This corresponds to a…
A (2+1)-dimensional growth process with explicit stationary measures
Fabio Lucio Toninelli
We introduce a class of (2+1)-dimensional stochastic growth processes, that can be seen as irreversible random dynamics of discrete interfaces. "Irreversible" means that the interf…
Multi-level pinning problems for random walks and self-avoiding lattice paths
Pietro Caputo, Fabio Martinelli, Fabio Lucio Toninelli
We consider a generalization of the classical pinning problem for integer-valued random walks conditioned to stay non-negative. More specifically, we take pinning potentials of the…