### Abstract

In these notes we try to review developments in the last decade of the theory on stochastic models for interfaces arising in two phase system, mostly on the so-called φ interface model. We are, in particular, interested in the scaling limits which pass from the microscopic models to macroscopic level. Such limit procedures are formulated as classical limit theorems in probability theory such as the law of large numbers, the central limit theorem and the large deviation principles.

Original language | English |
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Title of host publication | Lectures on Probability Theory and Statistics |

Subtitle of host publication | Ecole d'Ete de Probabilites de Saint-Flour XXXIII - 2003 |

Publisher | Springer Verlag |

Pages | 105-274 |

Number of pages | 170 |

Volume | 1869 |

ISBN (Print) | 3540260692, 9783540260691 |

Publication status | Published - 2005 |

Externally published | Yes |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 1869 |

ISSN (Print) | 0075-8434 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Lectures on Probability Theory and Statistics: Ecole d'Ete de Probabilites de Saint-Flour XXXIII - 2003*(Vol. 1869, pp. 105-274). (Lecture Notes in Mathematics; Vol. 1869). Springer Verlag.

**Stochastic interface models.** / Funaki, Tadahisa.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Lectures on Probability Theory and Statistics: Ecole d'Ete de Probabilites de Saint-Flour XXXIII - 2003.*vol. 1869, Lecture Notes in Mathematics, vol. 1869, Springer Verlag, pp. 105-274.

}

TY - CHAP

T1 - Stochastic interface models

AU - Funaki, Tadahisa

PY - 2005

Y1 - 2005

N2 - In these notes we try to review developments in the last decade of the theory on stochastic models for interfaces arising in two phase system, mostly on the so-called φ interface model. We are, in particular, interested in the scaling limits which pass from the microscopic models to macroscopic level. Such limit procedures are formulated as classical limit theorems in probability theory such as the law of large numbers, the central limit theorem and the large deviation principles.

AB - In these notes we try to review developments in the last decade of the theory on stochastic models for interfaces arising in two phase system, mostly on the so-called φ interface model. We are, in particular, interested in the scaling limits which pass from the microscopic models to macroscopic level. Such limit procedures are formulated as classical limit theorems in probability theory such as the law of large numbers, the central limit theorem and the large deviation principles.

UR - http://www.scopus.com/inward/record.url?scp=33746243519&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746243519&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:33746243519

SN - 3540260692

SN - 9783540260691

VL - 1869

T3 - Lecture Notes in Mathematics

SP - 105

EP - 274

BT - Lectures on Probability Theory and Statistics

PB - Springer Verlag

ER -