Relative complexity of random walks in random scenery in the absence of a weak invariance principle for the local times

• George Deligiannidis ^[1] ; Zemer Kosloff ^[2]
  1. [1] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
  2. [2] University of Warwick

     University of Warwick

     Reino Unido

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 4, 2017, págs. 2505-2532
• Idioma: inglés
• DOI: 10.1214/16-AOP1118
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• Resumen

  • We answer a question of Aaronson about the relative complexity of Random Walks in Random Sceneries driven by either aperiodic two-dimensional random walks, two-dimensional Simple Random walk, or by aperiodic random walks in the domain of attraction of the Cauchy distribution. A key step is proving that the range of the random walk satisfies the Fölner property almost surely.