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- W2058974098 abstract "We characterize non-decreasing weight functions for which the associated one-dimensional vertex reinforced random walk (VRRW) localizes on 4 sites. A phase transition appears for weights of order $nlog log n$: for weights growing faster than this rate, the VRRW localizes almost surely on at most 4 sites whereas for weights growing slower, the VRRW cannot localize on less than 5 sites. When $w$ is of order $nlog log n$, the VRRW localizes almost surely on either 4 or 5 sites, both events happening with positive probability." @default.
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- W2058974098 date "2012-09-08" @default.
- W2058974098 modified "2023-10-16" @default.
- W2058974098 title "Localization on $4$ sites for Vertex-reinforced random walks on $mathbb Z$." @default.
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