Renewal approach for the energy-momentum relation of the Fröhlich polaron

We study the qualitative behaviour of the energy-momentum relation of the Fröhlich polaron at fixed coupling strength. Among other properties, we show that it is non-decreasing and that the correction to the quasi-particle energy is negative. We give a proof that the effective mass lies in $(1,\mathrm{\infty })$ that does not need the validity of a central limit theorem for the path measure.