Power-law decay of weights and recurrence of the two-dimensional VRJP

Gady Kozma, Ron Peled

Research output: Contribution to journalArticlepeer-review


The vertex-reinforced jump process (VRJP) is a form of self-interacting random walk in which the walker is biased towards returning to previously visited vertices with the bias depending linearly on the local time at these vertices. We prove that, for any initial bias, the weights sampled from the magic formula on a two-dimensional graph decay at least at a power-law rate. Via arguments of Sabot and Zeng, the result implies that the VRJP is recurrent in two dimensions for any initial bias.

Original languageEnglish
Article number82
JournalElectronic Journal of Probability
StatePublished - 2021


FundersFunder number
Jesselson Foundation1971/19, 861/15
Horizon 2020 Framework Programme678520
European Research Council
Israel Science Foundation


    • Decay of correlations
    • Random walk in random environment
    • Supersymmetry
    • Vertex-reinforced jump process


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