Abstract:
We consider the symmetric inclusion process on a general finite graph. In the log-concave regime, we establish universal upper and lower bounds for the spectral gap of this process in terms of the spectral gap of the single-particle random walk, thereby verifying the celebrated Aldous' conjecture, originally formulated for the interchange process. Next, in the general non-log-concave regime, we prove that the conjecture does not hold by investigating the so-called metastable regime when the diffusivity constant vanishes in the limit. This talk is based on joint works with Federico Sau.
Biography:
Seonwoo Kim received his Ph.D. degree from Seoul National University in 2023. He was a Research Fellow at KIAS from 2023.09 to 2024.01, and is a June E Huh Fellow (KIAS Assistant Professor) at the same institute from 2024.02 to present. His recent research interests include metastability of large-scale systems, spectral gap and cutoff phenomenon of particle systems, and non-equilibrium fluctuations of interacting particle systems.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.