4 papers
Dimers with layered disorder
Quentin Moulard, Fabio Toninelli
We study the dimer model on the square grid, with quenched random edge weights. Randomness is chosen to have a layered structure, similar to that of the celebrated McCoy-Wu disorde…
Superdiffusive Central Limit Theorem for the Stochastic Burgers Equation at the critical dimension
Giuseppe Cannizzaro, Quentin Moulard, Fabio Toninelli
The Stochastic Burgers Equation (SBE) is a singular, non-linear Stochastic Partial Differential Equation (SPDE) that describes, on mesoscopic scales, the fluctuations of stochastic…
Convergence of dynamical stationary fluctuations
Cyril Labbé, Benoît Laslier, Fabio Toninelli +1
We present a general black box theorem that ensures convergence of a sequence of stationary Markov processes, provided a few assumptions are satisfied. This theorem relies on a con…
Lecture notes on stationary critical and super-critical SPDEs
Giuseppe Cannizzaro, Fabio Toninelli
The goal of these lecture notes is to present recent results regarding the large-scale behaviour of critical and super-critical non-linear stochastic PDEs, that fall outside the re…