### 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 |
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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

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

## Cite this

Arous, G. B., & Léandre, R. (1991). Décroissance exponentielle du noyau de la chaleur sur la diagonale (II).

*Probability Theory and Related Fields*,*90*(3), 377-402. https://doi.org/10.1007/BF01193751