7 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…
Hierarchy of KPZ limits arising from directed random walk models in random media
Shalin Parekh
We consider a generalized model of random walk in dynamical random environment, and we show that the multiplicative-noise stochastic heat equation (SHE) describes the fluctuations…
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…
Moment-based approach for two erratic KPZ scaling limits
Shalin Parekh
A recent paper of Tsai shows how the first few moments of a stochastic flow in the space of measures can completely determine its law. Here we give another proof of this result for…
Intermediate disorder for directed polymers with space-time correlations
Shalin Parekh
We revisit a result of Hairer-Shen on polymer-type approximations for the stochastic heat equation with a multiplicative noise (SHE) in . We consider a general class of polyme…
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…