### 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 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*395*(2), 437-447. https://doi.org/10.1016/j.jmaa.2012.04.076

**A probabilistic representation of the ground state expectation of fractional powers of the boson number operator.** / Hiroshima, Fumio; Lorinczi, József; Takaesu, Toshimitsu.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 395, no. 2, pp. 437-447. https://doi.org/10.1016/j.jmaa.2012.04.076

}

TY - JOUR

T1 - A probabilistic representation of the ground state expectation of fractional powers of the boson number operator

AU - Hiroshima, Fumio

AU - Lorinczi, József

AU - Takaesu, Toshimitsu

PY - 2012/11/15

Y1 - 2012/11/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84864024443&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864024443&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2012.04.076

DO - 10.1016/j.jmaa.2012.04.076

M3 - Article

VL - 395

SP - 437

EP - 447

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -