### Abstract

We consider the two dimensional discrete Gaussian free field confined between two hard walls. We show that the field becomes massive and identify the precise asymptotic behavior of the mass and the variance of the field as the height of the wall goes to infinity. By large fluctuation of the field, asymptotic behaviors of these quantities in the two dimensional case differ greatly from those of the higher dimensional case studied by [14].

Original language | English |
---|---|

Pages (from-to) | 2310-2327 |

Number of pages | 18 |

Journal | Electronic Journal of Probability |

Volume | 14 |

Publication status | Published - 2009 |

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### Keywords

- Gaussian field
- Hard wall
- Mass
- Random interface
- Random walk representation

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Confinement of the two dimensional discrete Gaussian free field between two hard walls.** / Sakagawa, Hironobu.

Research output: Contribution to journal › Article

*Electronic Journal of Probability*, vol. 14, pp. 2310-2327.

}

TY - JOUR

T1 - Confinement of the two dimensional discrete Gaussian free field between two hard walls

AU - Sakagawa, Hironobu

PY - 2009

Y1 - 2009

N2 - We consider the two dimensional discrete Gaussian free field confined between two hard walls. We show that the field becomes massive and identify the precise asymptotic behavior of the mass and the variance of the field as the height of the wall goes to infinity. By large fluctuation of the field, asymptotic behaviors of these quantities in the two dimensional case differ greatly from those of the higher dimensional case studied by [14].

AB - We consider the two dimensional discrete Gaussian free field confined between two hard walls. We show that the field becomes massive and identify the precise asymptotic behavior of the mass and the variance of the field as the height of the wall goes to infinity. By large fluctuation of the field, asymptotic behaviors of these quantities in the two dimensional case differ greatly from those of the higher dimensional case studied by [14].

KW - Gaussian field

KW - Hard wall

KW - Mass

KW - Random interface

KW - Random walk representation

UR - http://www.scopus.com/inward/record.url?scp=77956126234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956126234&partnerID=8YFLogxK

M3 - Article

VL - 14

SP - 2310

EP - 2327

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

ER -