The vacant set of two-dimensional critical random interlacement is infinite

• Francis Comets ^[1] ; Serguei Popov ^[2]
  1. [1] Université Denis Diderot

     Université Denis Diderot

     París, Francia

     
  2. [2] University of Campinas (Brasil)
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 2, 2017, págs. 4752-4785
• Idioma: inglés
• DOI: 10.1214/17-AOP1177
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• Resumen

  • For the model of two-dimensional random interlacements in the critical regime (i.e., α=1α=1), we prove that the vacant set is a.s. infinite, thus solving an open problem from [Commun. Math. Phys. 343 (2016) 129–164]. Also, we prove that the entrance measure of simple random walk on annular domains has certain regularity properties; this result is useful when dealing with soft local times for excursion processes.