Effective mass of the Fröhlich Polaron and the Landau–Pekar–Spohn conjecture

We prove that there is a constant $\overline C\in (0,\infty)$ such that the effective mass $m(α)$ of the Fröhlich Polaron satisfies $m(α) \geq \overline C α^4$, which is sharp according to a long-standing prediction of Landau-Pekar [19] from 1948 and of Spohn [36] from 1987. The method of proof, which demonstrates how the sharp quartic divergence rate of $m(α)$ appears in a natural way, is based on analyzing the Gaussian representation of the Polaron measure and that of the associated tilted Poisson point process developed in [26]. Additionally, our technique here leads to accompanying results including, 1) an explicit identification of local interval process from [26] in the strong coupling limit in terms of functionals of the Pekar process [27], 2) strict monotonicity of the effective mass $m(α)$ for all $α>0$ and 3) the quartic divergence of $m(α)$ for a generalized class of Polaron type interactions.