Anomalous diffusion of random walk on random planar maps

@article{Gwynne2020AnomalousDO,
  title={Anomalous diffusion of random walk on random planar maps},
  author={Ewain Gwynne and Tom Hutchcroft},
  journal={Probability Theory and Related Fields},
  year={2020}
}
We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most $$n^{1/4 + o_n(1)}$$ n 1 / 4 + o n ( 1 ) in n units of time. Together with the complementary lower bound proven by Gwynne and Miller (2017) this shows that the typical graph distance displacement of the walk after n steps is $$n^{1/4 + o_n(1)}$$ n 1 / 4 + o n ( 1 ) , as conjectured by Benjamini and Curien (Geom Funct Anal 2(2):501–531, 2013. arXiv… 
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