68 citations · 89 across the 14 of their papers we have counts for
14 papers · 1 filter
A universality result for the critical 2d stochastic heat flow
Hindy Drillick, Jonathan Hou, Shalin Parekh
For a large class of discrete- and continuous-time models satisfying a linear flow property, we prove convergence to the critical stochastic heat flow under diffusive scaling…
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…
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…
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…
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…
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…
A nonlinear Strassen law for singular SPDEs
Shalin Parekh
A result of Arcones implies that if a measure-preserving linear operator on an abstract Wiener space is strongly mixing, then the set of limit points of the random se…
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…
Ergodicity results for the open KPZ equation
Shalin Parekh
We give a new proof of existence as well as two proofs of uniqueness of the invariant measure of the open-boundary KPZ equation on [0,1], for all possible choices of inhomogeneous…
Convergence of ASEP to KPZ with basic coupling of the dynamics
Shalin Parekh
We prove an extension of a seminal result of Bertini and Giacomin. Namely we consider weakly asymmetric exclusion processes with several distinct initial data simultaneously, then…
Limit Shape of Subpartition Maximizing Partitions
Ivan Corwin, Shalin Parekh
This is an expository note answering a question posed to us by Richard Stanley, in which we prove a limit shape theorem for partitions of which maximize the number of subpartit…
Positive random walks and an identity for half-space SPDEs
Shalin Parekh
The purpose of this article is threefold. First, we introduce a new type of boundary condition for the multiplicative-noise stochastic heat equation on the half space. This is esse…
The KPZ Limit of ASEP with Boundary
Shalin Parekh
It was recently proved in [Corwin-Shen, 2016] that under weak asymmetry scaling, the height functions for open ASEP on the half-line and on a bounded interval converge to the Hopf-…