Rishabh Gvalani's home page

I am a post-doctoral research associate 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. I am broadly interested in PDEs and probability.

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. [arXiv]
  3. with Benjamin Gess and Vitalii Konarovskyi. Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent. [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. [arXiv]
  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]