Rishabh Gvalani's home page


I am a SwissMAP research fellow at ETH Zürich. Before this, I was a postdoc at the Max Planck Institute in Leipzig in the groups of Benjamin Gess and Felix Otto. I obtained my PhD in Mathematics in June, 2020 from Imperial College London, under the supervision of Greg Pavliotis and José Antonio Carrillo.


My research lies at the intersection of PDEs and probability. I am interested in interacting particle systems, SPDEs, large deviations, optimal transport, random dynamical systems, and some aspects of incompressible fluids (mixing, enhanced dissipation, etc.).

Publications and preprints

  1. with Markus Tempelmayr. Stochastic estimates for the thin-film equation with thermal noise. [arXiv]
  2. with Michele Coti Zelati and Theodore D. Drivas. Statistically self-similar mixing by Gaussian random fields. J. Stat. Phys., 2024. [arXiv | doi]
  3. with Benjamin Gess and Vitalii Konarovskyi. Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent. Probab. Theory Related Fields, 2025, to appear. [arXiv]
  4. with Benjamin Ferhman and Benjamin Gess. Ergodicity and random dynamical systems for conservative SPDEs. [arXiv]
  5. with Alex Blumenthal and Michele Coti Zelati. Exponential mixing for random dynamical systems and an example of Pierrehumbert. Ann. Prob., 2023 [arXiv | doi]
  6. with Antonio Esposito, André Schlichting, and Markus Schmidtchen. On a novel gradient flow structure for the aggregation equation. Calc. Var. Partial Diff., 2024 [arXiv | doi]
  7. with Matías G. Delgadino, Grigorios A. Pavliotis, and Scott A. Smith. Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions. Comm. Math. Phys., 2023 [arXiv | doi]
  8. with Benjamin Gess, Florian Kunick, and Felix Otto. Thermodynamically consistent and positivity preserving discretization of the thin-film equation with thermal noise. Math. Comp., 2023 [arXiv | doi]
  9. with José A. Carrillo and Jeremy Wu. An invariance principle for gradient flows in the space of probability measres. J. Differential Equations, 2022 [arXiv | doi]
  10. with Matías G. Delgadino and Grigorios A. Pavliotis. On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions. Arch. Ration. Mech. Anal., 2021 [arXiv | doi]
  11. with José A. Carrillo. Phase transitions in nonlinear nonlocal aggregation-diffusion equations. Comm. Math. Phys., 2021. [arXiv | doi]
  12. with André Schlichting. Barriers of the McKean-Vlasov energy via a mountain pass theorem in the space of probability measures. J. Funct. Anal., 2020. [arXiv | doi]
  13. with José A. Carrillo, Grigorios A. Pavliotis, and André Schlichting. Long-time behaviour and phase transitions for the McKean–Vlasov equation on the torus. Arch. Ration. Mech. Anal., 2020. [arXiv | doi]
  14. with Miguel A. Durán-Olivenca, Serafim Kalliadasis, and Grigorios A. Pavliotis. Instability, Rupture and Fluctuations in Thin Liquid Films: Theory and Computations. J. Stat. Phys., 2018. [arXiv | doi]