I am Shalin Parekh, a NSF postdoc in math 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
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11. Moment-based approach for two erratic KPZ scaling limits.
Submitted, 2024. (arXiv)
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10. The directed landscape is a black noise.
with Zoe Himwich.
Submitted, 2024. (arXiv)
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9. Hierarchy of KPZ scaling limits arising from directed random walk models in random media.
Submitted, 2024. (arXiv)
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8. KPZ equation limit of random walks in random environments.
with Sayan Das and Hindy Drillick.
Probab. Th. Rel Fields (to appear). (arXiv)
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7. A nonlinear Strassen law for singular SPDEs.
Electron. J. Probab. 2024. (arXiv)
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6. KPZ equation limit of sticky Brownian motion,
with Sayan Das and Hindy Drillick.
J. Funct. Analysis (to appear). (arXiv)
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5. Ergodicity results for the open KPZ equation.
Ann. IHP Probab. et Stat. (to appear) . (arXiv)
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4. Convergence of ASEP to KPZ with basic coupling of the dynamics.
Stoch. Proc. Appl., 2022. (arXiv)
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3. Limit shape of subpartition-maximizing partitions,
with Ivan Corwin.
J. Stat. Phys, 2020.
(arXiv)
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2. Positive random walks and an identity for half-space SPDEs.
Electron. J. Probab., 2022. (arXiv)
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1. The KPZ limit of ASEP with boundary.
Comm. Math. Phys., 2018. (arXiv)
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