15/01/2025, 16:00 — 17:00 — Online
Seonwoo Kim, Kias, Seoul
Spectral gap of the symmetric inclusion process: Aldous' conjecture and metastability
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.
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