Research
The main focus of my research has been asymptotic problems arising from Branching Processes, Branching Diffusions and related Dynamical Systems. The central theme in most of my work is the use of spectral theory in addition to techniques from probability, stochastic differential equations, parabolic partial differential equations, homogenization theory, and dynamical systems to obtain the asymptotics of these stochastic processes that are valid up to the domain of large deviations.
Publications
Articles under peer review:
- P. Hebbar, L. Koralov “Distribution of particles at and near the front in supercritical branching Brownian motion with compactly supported branching“ (2026).
Published Journal Articles:
- L. Ajax, B. Durham, P. Hebbar, C. Johnston, M. Zhang “Inhomogeneous Branching Random Walks: Incorporating Genealogy and Density Effects“ Spora: A Journal of Biomathematics: Vol. 12, 1–16. doi:10.61403/2473-5493.1112 (2025) *in collaboration with undergraduate students.
- P. Hebbar, K. Fernando, Higher order asymptotics for large deviations — Part II, Stochastics and Dynamics, Vol. 21, No. 05, 2150025, (2021)
- P. Hebbar, L. Koralov, J. Nolen, Asymptotic behavior of branching diffusion processes in periodic media, Electronic Journal of Probability, vol. 25, paper no. 126, 40 pp doi:10.1214/20-EJP527 (2020)
- P. Hebbar, K. Fernando, Higher order asymptotics for large deviations — Part I, Asymptotic Analysis, vol. Pre-press, pp. 1-39, (2020). doi:10.3233/ASY-201602.
- D.Dolgopyat, P. Hebbar, L. Koralov, M. Perlman, “Multi-type branching processes with time-dependent branching rates“, Journal of Applied Probability, 55(3), 701-727. doi:10.1017/jpr.2018.46, (2018)
Ph.D Dissertation
- Branching diffusion processes in periodic media, Thesis, August 2019.
Book Reviews
- Hebbar P. “Testing the waters of differential equations“, Physics Today, Volume 73, Issue 7, Page 54 (2020). doi.org/10.1063/PT.3.4525
