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- W4295988087 abstract "We derive new HWI inequalities for the granular media equation, which external potential $V$ and interaction potential $W$ are only strictly convex on complementary parts of the space. Particularly, potentials are not assumed convex. After solving technicalities related to the singularity of a logarithmic $W$, we apply our result to obtain stability rates of log gases under non-strictly convex or quartic external potentials. We prove that the distribution of a log gas converges towards an equilibrium with respect to the Wasserstein distance at a square root rate. Finally, we establish exponential stability of log gases under the double-well potential $V(x) = frac{x^4}{4} + cfrac{x^2}{2}$, $c < 0$ and the non-confining potential $V(x) = gfrac{x^4}{4} + frac{x^2}{2}$, $g<0$ for $|c|$ and $|g|$ small enough." @default.
- W4295988087 created "2022-09-16" @default.
- W4295988087 creator A5032137838 @default.
- W4295988087 date "2020-11-17" @default.
- W4295988087 modified "2023-09-27" @default.
- W4295988087 title "Trend to equilibrium for granular media equations under non-convex potential and application to log gases" @default.
- W4295988087 doi "https://doi.org/10.48550/arxiv.2011.08547" @default.
- W4295988087 hasPublicationYear "2020" @default.
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