6 papers
The critical KPZ scale for the Averaging Process
Hindy Drillick, Shalin Parekh, Federico Sau
KPZ-type extremal fluctuations have recently been proved for several models of random walks in space-time random environments (RWRE) in dimensions. A general moment criterion…
Random walks in space-time random media in all spatial dimensions: the full subcritical fluctuation regime
Hindy Drillick, Shalin Parekh
In arbitrary spatial dimension , we study a generalized model of random walks in a time-varying random environment (RWRE) defined by a stochastic flow of kernels. We consid…
Universal KPZ Fluctuations for Moderate Deviations of Random Walks in Random Environments
Jacob Hass, Hindy Drillick, Ivan Corwin +1
The theory of diffusion seeks to describe the motion of particles in a chaotic environment. Classical theory models individual particles as independent random walkers, effectively…
The stochastic six-vertex model speed process
Hindy Drillick, Levi Haunschmid-Sibitz
For the stochastic six-vertex model on the quadrant with step initial conditions and a single second-class particle at the origin, we s…
KPZ equation limit of sticky Brownian motion
Sayan Das, Hindy Drillick, Shalin Parekh
We consider the motion of a particle under a continuum random environment whose distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we establish that…
Multiplicative SHE limit of random walks in space-time random environments
Sayan Das, Hindy Drillick, Shalin Parekh
We show that under a certain moderate deviation scaling, the multiplicative-noise stochastic heat equation (SHE) arises as the fluctuations of the quenched density of a 1D random w…