Title of the talk: Spectral Theory and Brownian Motion on Quantum Graphs

Date , Time & Venue: 18 July 2025, 11:00 AM 

Abstract: Brownian motion on quantum graphs provides a rich interplay between probability theory, spectral analysis, and mathematical physics. This talk examines diffusion processes on the simplest quantum graph — the star (or spider) graph — consisting of multiple semi-infinite edges joined at a single vertex with Kirchhoff’s gluing conditions. We derive explicit transition probabilities, first exit time distributions, and limit theorems that generalize classical results such as Lévy’s arcsine law and the Erdős–Rényi covering time. These findings illustrate how randomness interacts with quantum geometry and highlight connections to the spectral theory of Schrödinger operators, with implications for wave propagation, nanostructures, and the inverse spectral problem.

About the Speaker: Dr. Madhumita Paul is currently working as  Research Assistant  at UNC-Charlotte. She obtained Ph.D (2017-2023, Advisor- Stanislav Molchanov) from UNC-Charlotte, and her research area is "spectral theory of the Schrodinger operator," which studies different types of potentials, eg:- periodic potentials, unbounded potentials, etc. We look forward to your presence in the seminar.