Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.

Francis Nier[1]

  • [1] IRMAR, Université de Rennes 1, Campus de Beaulieu, F-35042 Rennes Cedex, France.

Journées Équations aux dérivées partielles (2004)

  • page 1-17
  • ISSN: 0752-0360

Abstract

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We present here a simplified version of recent results obtained with B. Helffer and M. Klein. They are concerned with the exponentally small eigenvalues of the Witten Laplacian on 0 -forms. We show how the Witten complex structure is better taken into account by working with singular values. This provides a convenient framework to derive accurate approximations of the first eigenvalues of Δ f , h ( 0 ) and solves efficiently the question of weakly resonant wells.

How to cite

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Nier, Francis. "Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.." Journées Équations aux dérivées partielles (2004): 1-17. <http://eudml.org/doc/10600>.

@article{Nier2004,
abstract = {We present here a simplified version of recent results obtained with B. Helffer and M. Klein. They are concerned with the exponentally small eigenvalues of the Witten Laplacian on $0$-forms. We show how the Witten complex structure is better taken into account by working with singular values. This provides a convenient framework to derive accurate approximations of the first eigenvalues of $\Delta _\{f,h\}^\{(0)\}$ and solves efficiently the question of weakly resonant wells.},
affiliation = {IRMAR, Université de Rennes 1, Campus de Beaulieu, F-35042 Rennes Cedex, France.},
author = {Nier, Francis},
journal = {Journées Équations aux dérivées partielles},
keywords = {exponentially small eigenvalues; Witten Laplacian; Witten complex structure; weakly resonant wells},
language = {eng},
month = {6},
pages = {1-17},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.},
url = {http://eudml.org/doc/10600},
year = {2004},
}

TY - JOUR
AU - Nier, Francis
TI - Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.
JO - Journées Équations aux dérivées partielles
DA - 2004/6//
PB - Groupement de recherche 2434 du CNRS
SP - 1
EP - 17
AB - We present here a simplified version of recent results obtained with B. Helffer and M. Klein. They are concerned with the exponentally small eigenvalues of the Witten Laplacian on $0$-forms. We show how the Witten complex structure is better taken into account by working with singular values. This provides a convenient framework to derive accurate approximations of the first eigenvalues of $\Delta _{f,h}^{(0)}$ and solves efficiently the question of weakly resonant wells.
LA - eng
KW - exponentially small eigenvalues; Witten Laplacian; Witten complex structure; weakly resonant wells
UR - http://eudml.org/doc/10600
ER -

References

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