A lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles

Abstract

<p style='text-indent:20px;'>In this paper, we proceed as suggested in the final section of [<xref ref-type="bibr" rid="b2">2</xref>] and prove a lower bound for the spectral gap of the conjugate Kac process with 3 interacting particles. This bound turns out to be around <inline-formula><tex-math id="M1">\begin{document}$ 0.02 $\end{document}</tex-math></inline-formula>, which is already physically meaningful, and we perform Monte Carlo simulations to provide a better empirical estimate for this value via entropy production inequalities. This finishes a complete quantitative estimate of the spectral gap of the Kac process.</p>