Hindy Drillick

A universality result for the critical 2d stochastic heat flow

For a large class of discrete- and continuous-time models satisfying a linear flow property, we prove convergence to the critical $2d$ stochastic heat flow under diffusive scaling of space and time. Convergence is in the sense of finite-dimensional distributions in the space of measure-valued stochastic flows. The clas...

The critical KPZ scale for the Averaging Process

KPZ-type extremal fluctuations have recently been proved for several models of random walks in space-time random environments (RWRE) in $1+1$ dimensions. A general moment criterion predicts the spatial scale at which this behavior should occur, but does not by itself guarantee non-trivial fluctuations at that scale. In...

Universal Kardar-Parisi-Zhang fluctuations for moderate deviations of random walks in random environments