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dc.contributor.authorPeterson, Jonathon
dc.contributor.authorSamorodnitsky, Gennady
dc.description.abstractWe consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter kappa>0 that determines the fluctuations of the process. When 0<kappa<2, the averaged distributions of the hitting times of the random walk converge to a kappa-stable distribution. However, it was shown recently that in this case there does not exist a quenched limiting distribution of the hitting times. That is, it is not true that for almost every fixed environment, the distributions of the hitting times (centered and scaled in any manner) converge to a non-degenerate distribution. We show, however, that the quenched distributions do have a limit in the weak sense. That is, the quenched distributions of the hitting times %of the random walk -- viewed as a random probability measure on R -- converge in distribution to a random probability measure, which has interesting stability properties. Our results generalize both the averaged limiting distribution and the non-existence of quenched limiting distributions.en_US
dc.description.sponsorshipJ. Peterson was partially supported by National Science Foundation grant DMS-0802942. G. Samorodnitsky was partially supported by ARO grant W911NF-10-1-0289 and NSF grant DMS-1005903 at Cornell Universityen_US
dc.subjectweak quenched limitsen_US
dc.subjectpoint processen_US
dc.subjectheavy tailsen_US
dc.titleWeak quenched limiting distributions for transient one-dimensional random walk in a random environmenten_US
dc.typetechnical reporten_US

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