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Splitting in Large Dimension and Infrared Estimates

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Microlocal Analysis and Spectral Theory

Part of the book series: NATO ASI Series ((ASIC,volume 490))

Abstract

These notes for the NATO ASI conference in Microlocal analysis and spectral theory consist in the analysis of the links between estimating the splitting between the two first eigenvalues for the Schrödinger operator and the proof of infrared estimates for quantities attached to Gaussian type measures. They are mainly based on the “old” contributions of Dyson, Fröhlich, Glimm, Jaffe, Lieb, Simon, Spencer (in the seventie’s) in connection with more recent contributions of Pastur, Khoruzhenko, Barbulyak, Kondratev which treat in general more sophisticated models. We shall show how the recent semi-classical analysis permits sometimes to state more precise results.

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Author information

Authors and Affiliations

  1. UA 760 du CNRS, Département de mathématiques, Bât 425, F-91405, Orsay Cédex, France

    B. Helffer

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  1. B. Helffer
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Editors and Affiliations

  1. Department of Mathematics, University of Torino, Torino, Italy

    Luigi Rodino

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Helffer, B. (1997). Splitting in Large Dimension and Infrared Estimates. In: Rodino, L. (eds) Microlocal Analysis and Spectral Theory. NATO ASI Series, vol 490. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5626-4_10

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  • DOI: https://doi.org/10.1007/978-94-011-5626-4_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6371-5

  • Online ISBN: 978-94-011-5626-4

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