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- W2000334782 abstract "We consider a vertex reinforced random walk on the integer lattice with sub-linear reinforcement. Under some assumptions on the regular variation of the weight function, we characterize whether the walk gets stuck on a finite interval. When this happens, we estimate the size of the localization set. In particular, we show that, for any odd number $$N$$ larger than or equal to $$5$$ , there exists a vertex reinforced random walk which localizes with positive probability on exactly $$N$$ consecutive sites." @default.
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- W2000334782 date "2013-04-27" @default.
- W2000334782 modified "2023-10-16" @default.
- W2000334782 title "Localization of a vertex reinforced random walk on $$mathbb{Z }$$ with sub-linear weight" @default.
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- W2000334782 doi "https://doi.org/10.1007/s00440-013-0502-3" @default.
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