Abstract: In this talk we will review some recent results on the Fröhlich polaron, which is a model for a charged particle coupled to a polarizable medium. We will especially focus on a conjecture due to Landau and Pekar from 1948, claiming that the mass of the charged particle is effectively increased due to its interaction with the environment according to the asymptotic formula m_eff=\alpha^4 m_LP, where \alpha is the coupling strength between particle and medium and m_LP is an explicit constant. Notably the recent progress is due to two rather distinct approaches, one working with functional integration (probabilistic/commutative) and the other one working with functional analytic methods (operator theory/non-commutative), which are connected by the celebrated Feynman-Kac formula.

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