
Random Walk on a Perturbation of the Infinitely-Fast Mixing Interchange Process
Salvi, Michele; Simenhaus, François (2018), Random Walk on a Perturbation of the Infinitely-Fast Mixing Interchange Process, Journal of Statistical Physics, 171, 4, p. 656-678. 10.1007/s10955-018-2015-z
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Article accepté pour publication ou publiéDate
2018Journal name
Journal of Statistical PhysicsVolume
171Number
4Publisher
Springer
Pages
656-678
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Show full item recordAuthor(s)
Salvi, MicheleCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Simenhaus, François
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider a random walk in dimension d≥1 in a dynamic random environment evolving as an interchange process with rate γ>0. We prove that, if we choose γ large enough, almost surely the empirical velocity of the walker Xt/t eventually lies in an arbitrary small ball around the annealed drift. This statement is thus a perturbation of the case γ=+∞ where the environment is refreshed between each step of the walker. We extend three-way part of the results of Huveneers and Simenhaus (Electron J Probab 20(105):42, 2015), where the environment was given by the 1-dimensional exclusion process: (i) We deal with any dimension d≥1; (ii) We treat the much more general interchange process, where each particle carries a transition vector chosen according to an arbitrary law μ; (iii) We show that Xt/t is not only in the same direction of the annealed drift, but that it is also close to it.Subjects / Keywords
Random walk; Dynamic random environment; Interchange process; Limit theorems; RenormalisationRelated items
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