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Parabolic problems for the Anderson model
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  • Published: June 1998

Parabolic problems for the Anderson model

II. Second-order asymptotics and structure of high peaks★

  • J. Gärtner1 &
  • S. A. Molchanov2 

Probability Theory and Related Fields volume 111, pages 17–55 (1998)Cite this article

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Summary.

This is a continuation of our previous work [6] on the investigation of intermittency for the parabolic equation (∂/∂t)u=Hu on ℝ+×ℤd associated with the Anderson Hamiltonian H=κΔ+ξ(·) for i.i.d. random potentials ξ(·). For the Cauchy problem with nonnegative homogeneous initial condition we study the second order asymptotics of the statistical moments <u(t,0)p> and the almost sure growth of u(t,0) as t→∞. We point out the crucial role of double exponential tails of ξ(0) for the formation of high intermittent peaks of the solution u(t,·) with asymptotically finite size. The challenging motivation is to achieve a better understanding of the geometric structure of such high exceedances which in one or another sense provide the essential contribution to the solution.

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Authors and Affiliations

  1. Technische Universität, FB Mathematik, Strasse des 17. Juni 136, D-10623 Berlin, Germany e-mail: jg@math.tu-berlin.de, , , , , , DE

    J. Gärtner

  2. Department of Mathematics, University of North Carolina, Charlotte, NC 28223-9998, USA, , , , , , US

    S. A. Molchanov

Authors
  1. J. Gärtner
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  2. S. A. Molchanov
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Received: 10 December 1996 / In revised form: 30 September 1997

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Gärtner, J., Molchanov, S. Parabolic problems for the Anderson model . Probab Theory Relat Fields 111, 17–55 (1998). https://doi.org/10.1007/s004400050161

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  • Issue Date: June 1998

  • DOI: https://doi.org/10.1007/s004400050161

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  • Mathematics Subject Classification (1991): Primary 60H25
  • 82C44; Secondary 60F10
  • 60K40
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