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Some connections between excursion theory and the discrete Schrödinger equation with random potentials
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  • Published: May 1987

Some connections between excursion theory and the discrete Schrödinger equation with random potentials

  • Peter March1 nAff2 &
  • Alain-Sol Sznitman2,3 

Probability Theory and Related Fields volume 75, pages 11–53 (1987)Cite this article

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Summary

We use here discrete excursion theory, and the Ray-Knight theorem, in order to study questions concerning the analyticity of the density of states at “low disorder”, as well as its smoothness properties, in one dimension.

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Author information

Author notes
  1. Peter March

    Present address: Department of Mathematics, Mc Gill University, 805 Sherbrooke St. West, H3A2K6, Montreal, Quebec, Canada

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA

    Peter March

  2. Courant Institute of Mathematical Sciences, Université Paris VI, Associé au CNRS no 224, Tour 56, 4 place Jussieu, F-75005, Paris, France

    Alain-Sol Sznitman

  3. Laboratoire de Probabilités, Université Paris VI, Associé au CNRS no 224, Tour 56, 4 place Jussieu, F-75005, Paris, France

    Alain-Sol Sznitman

Authors
  1. Peter March
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  2. Alain-Sol Sznitman
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Additional information

Research supported in part by the grants NSF-MCS-82-01599 and DAAG6-84-K-0155

Research partially supported by grant AFOSR-85-0017 from the Air Force Office of Scientific Research

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Cite this article

March, P., Sznitman, AS. Some connections between excursion theory and the discrete Schrödinger equation with random potentials. Probab. Th. Rel. Fields 75, 11–53 (1987). https://doi.org/10.1007/BF00320079

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  • Received: 10 November 1985

  • Issue Date: May 1987

  • DOI: https://doi.org/10.1007/BF00320079

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Random Potential
  • Smoothness Property
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