Almost quartic lower bound for the Fröhlich polaron’s effective mass via Gaussian domination

We prove the Fröhlich polaron has effective mass at least $\frac{α^4}{(\log α)^6}$ when the coupling strength $α$ is large. This nearly matches the quartic growth rate $C_*α^4$ predicted by Landau and Pekar in 1948 and complements a recent sharp upper bound of Brooks and Seiringer. Our proof works with the path integral formulation of the problem and systematically applies the Gaussian correlation inequality to exploit quasi-concavity of the interaction terms.