I am Shalin Parekh, a math postdoc at UMD College Park.

Broadly speaking, I am interested in probability theory and its applications. Currently, I am thinking about anomalous fluctuations arising from random walks in random media.

You can reach me at parekh [at] umd [dot] edu. If you're at Maryland, visit me in office 2303 Kirwan Hall!

Here is a rough CV.

## Research

10. The directed landscape is a black noise.
*with Zoe Himwich.*
**Preprint, 2024.** (arXiv)

9. Invariance principle for the KPZ equation arising in stochastic flows of kernels.
**Submitted, 2024.** (arXiv)

8. KPZ equation limit of random walks in random environments.
*with Sayan Das and Hindy Drillick.*
**Submitted, 2023.** (arXiv)

7. A nonlinear Strassen law for singular SPDEs.
**Submitted, 2023.** (arXiv)

6. KPZ equation limit of sticky Brownian motion,
*with Sayan Das and Hindy Drillick.*
**Submitted, 2023.** (arXiv)

5. Ergodicity results for the open KPZ equation.
**to appear Ann. Inst. H. Poincare Probab. et Stat., 2024.** (arXiv)

4. Convergence of ASEP to KPZ with basic coupling of the dynamics.
**Stoch. Proc. Appl., 2022.** (arXiv)

3. Limit shape of subpartition-maximizing partitions,
*with Ivan Corwin.*
**J. Stat. Phys, 2020. **
(arXiv)

2. Positive random walks and an identity for half-space SPDEs.
**Electron. J. Probab., 2022. ** (arXiv)

1. The KPZ limit of ASEP with boundary.
** Comm. Math. Phys., 2018.** (arXiv)