A phase transition in the Bakry-Émery gradient estimate for Dyson Brownian motion

2025/06/04 by Suzuki, Kohei, Tashiro, Kenshiro · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.04424

Abstract

In this paper, we find a gap between the lower bound of the Bakry-Émery N-Ricci tensor \rm Ric_N and the Bakry-Émery gradient estimate \sf BE in the space associated with the finite-particle Dyson Brownian motion (DBM) with inverse temperature 0<β<1. Namely, we prove that, for the weighted space (\mathbb Rⁿ, w_β) with w_β=∏_i

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