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Lyapounov norms for random walks in low disorder and dimension greater than three
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  • Published: 12 February 2008

Lyapounov norms for random walks in low disorder and dimension greater than three

  • N. Zygouras1 

Probability Theory and Related Fields volume 143, pages 615–642 (2009)Cite this article

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Abstract

We consider a simple random walk on Z d, d > 3. We also consider a collection of i.i.d. positive and bounded random variables \(\left(V_\omega(x)\right)_{x\in Z^d}\) , which will serve as a random potential. We study the annealed and quenched cost to perform long crossing in the random potential \(-(\lambda+\beta V_\omega(x))\) , where λ is positive constant and β > 0 is small enough. These costs are measured by the Lyapounov norms. We prove the equality of the annealed and the quenched norm.

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Authors and Affiliations

  1. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, USA

    N. Zygouras

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  1. N. Zygouras
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Correspondence to N. Zygouras.

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Cite this article

Zygouras, N. Lyapounov norms for random walks in low disorder and dimension greater than three. Probab. Theory Relat. Fields 143, 615–642 (2009). https://doi.org/10.1007/s00440-008-0139-9

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  • Received: 14 May 2007

  • Revised: 12 December 2007

  • Published: 12 February 2008

  • Issue Date: March 2009

  • DOI: https://doi.org/10.1007/s00440-008-0139-9

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Keywords

  • Random walks
  • Random potential
  • Lyapounov norms
  • Mass gap estimate

Mathematics Subject Classification (2000)

  • 60xx
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