### Abstract

We consider the Fröhlich model of the polaron, whose path integral formulation leads to the transformed path measure (Formula presented.) with respect to ℙ that governs the law of the increments of the three-dimensional Brownian motion on a finite interval [−T, T], and Z_{α, T} is the partition function or the normalizing constant and α > 0 is a constant, or the coupling parameter. The polaron measure reflects a self-attractive interaction. According to a conjecture of Pekar that was proved in [9], (Formula presented.) exists and has a variational formula. In this article we show that when α > 0 is either sufficiently small or sufficiently large, the limit (Formula presented.) exists, which is also identified explicitly. As a corollary, we deduce the central limit theorem for (Formula presented.) under (Formula presented.) and obtain an expression for the limiting variance.

Original language | English (US) |
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Pages (from-to) | 350-383 |

Number of pages | 34 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 73 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2020 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorem for Large Times'. Together they form a unique fingerprint.

## Cite this

*Communications on Pure and Applied Mathematics*,

*73*(2), 350-383. https://doi.org/10.1002/cpa.21858