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Décroissance exponentielle du noyau de la chaleur sur la diagonale (II)
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  • Published: September 1991

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

  • G. Ben Arous1 &
  • R. Léandre2 

Probability Theory and Related Fields volume 90, pages 377–402 (1991)Cite this article

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Summary

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).

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Authors and Affiliations

  1. Département de mathématiques, Université Paris Sud, F-91405, Orsay, France

    G. Ben Arous

  2. Département de mathématiques, Université Louis Pasteur, rue Descartes, F-67084, Strasbourg, France

    R. Léandre

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  1. G. Ben Arous
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  2. R. Léandre
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Arous, G.B., Léandre, R. Décroissance exponentielle du noyau de la chaleur sur la diagonale (II). Probab. Th. Rel. Fields 90, 377–402 (1991). https://doi.org/10.1007/BF01193751

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  • Received: 03 March 1988

  • Revised: 09 July 1991

  • Issue Date: September 1991

  • DOI: https://doi.org/10.1007/BF01193751

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