### Abstract

We give some conditions for the heat kernel to have an asymptotic expansion in small time such that all coefficients vanish, although the phenomenon seems difficult to understand by large deviations theory. The fact that the leading term is not zero is strongly related to Bismut's condition. These examples are related to the Varadhan estimates of the density of a dynamical system submitted to small random perturbations. To understand that type of asymptotic, one must modify the definition of the distance by adding the Bismut condition (unnoticed, but hidden, in classical cases).

Original language | French |
---|---|

Pages (from-to) | 377-402 |

Number of pages | 26 |

Journal | Probability Theory and Related Fields |

Volume | 90 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1991 |

### ASJC Scopus subject areas

- Statistics and Probability
- Analysis
- Mathematics(all)

### Cite this

*Probability Theory and Related Fields*,

*90*(3), 377-402. https://doi.org/10.1007/BF01193751

**Décroissance exponentielle du noyau de la chaleur sur la diagonale (II).** / Arous, G. Ben; Léandre, R.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 90, no. 3, pp. 377-402. https://doi.org/10.1007/BF01193751

}

TY - JOUR

T1 - Décroissance exponentielle du noyau de la chaleur sur la diagonale (II)

AU - Arous, G. Ben

AU - Léandre, R.

PY - 1991/9

Y1 - 1991/9

N2 - We give some conditions for the heat kernel to have an asymptotic expansion in small time such that all coefficients vanish, although the phenomenon seems difficult to understand by large deviations theory. The fact that the leading term is not zero is strongly related to Bismut's condition. These examples are related to the Varadhan estimates of the density of a dynamical system submitted to small random perturbations. To understand that type of asymptotic, one must modify the definition of the distance by adding the Bismut condition (unnoticed, but hidden, in classical cases).

AB - We give some conditions for the heat kernel to have an asymptotic expansion in small time such that all coefficients vanish, although the phenomenon seems difficult to understand by large deviations theory. The fact that the leading term is not zero is strongly related to Bismut's condition. These examples are related to the Varadhan estimates of the density of a dynamical system submitted to small random perturbations. To understand that type of asymptotic, one must modify the definition of the distance by adding the Bismut condition (unnoticed, but hidden, in classical cases).

UR - http://www.scopus.com/inward/record.url?scp=33847299320&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33847299320&partnerID=8YFLogxK

U2 - 10.1007/BF01193751

DO - 10.1007/BF01193751

M3 - Article

AN - SCOPUS:33847299320

VL - 90

SP - 377

EP - 402

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3

ER -