### Abstract

We give a formula in terms of a joint Gibbs measure on Brownian paths and the measure of a random-time Poisson process of the ground state expectations of fractional (in fact, any real) powers of the boson number operator in the Nelson model. We use this representation to obtain tight two-sided bounds. As applications, we discuss the polaron and translation invariant Nelson models.

Original language | English |
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Pages (from-to) | 437-447 |

Number of pages | 11 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 395 |

Issue number | 2 |

DOIs | |

Publication status | Published - Nov 15 2012 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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## Cite this

Hiroshima, F., Lorinczi, J., & Takaesu, T. (2012). A probabilistic representation of the ground state expectation of fractional powers of the boson number operator.

*Journal of Mathematical Analysis and Applications*,*395*(2), 437-447. https://doi.org/10.1016/j.jmaa.2012.04.076