# 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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