Work

Spectral gap of the symmetric inclusion process

Year: 2024

Type: article

Abstract: We consider the symmetric inclusion process on a general finite graph. Our main result establishes universal upper and lower bounds for the spectral gap of this interacting particle system in terms of the spectral gap of the random walk on the same graph. In the regime in which the gamma-like reversible measures of the particle systems are log-concave, our bounds match, yielding a version for the symmetric inclusion process of the celebrated Aldous’ spectral gap conjecture originally formulated for the interchange process. Finally, by means of duality techniques, we draw analogous conclusions for an interacting diffusion-like unbounded conservative spin system known as Brownian energy process.

Source: The Annals of Applied Probability

DOI: 10.1214/24-aap2085

Authors: Seonwoo Kim, Federico Sau

Institutions: Korea Institute for Advanced Study, University of Trieste

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Institute of Science and Technology Austria, National Research Foundation, National Research Foundation of Korea, Ministry of Science and ICT, South Korea

Awards: G6627034725, G6947114504, G7116881531