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On the most visited sites of planar Brownian motion

   
@article{ECP1809,
	author = {Valentina Cammarota and Peter Mörters},
	title = {On the most visited sites of planar Brownian motion},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {17},
	year = {2012},
	keywords = {Brownian motion, Hausdorff dimension, Hausdorff gauge, local time, point of infinite multiplicity, uniform dimension estimates.},
	abstract = {
Let $(B_t \colon t \ge 0)$ be a planar Brownian motion and define gauge functions $\phi_\alpha(s)=\log(1/s)^{-\alpha}$ for $\alpha>0$. If $\alpha<1$ we show that almost surely there exists a point $x$ in the plane such that ${\mathcal H}^{\phi_\alpha}(\{t \ge 0 \colon B_t=x\})>0$,but if $\alpha>1$ almost surely ${\mathcal H}^{\phi_\alpha} (\{t \ge 0 \colon B_t=x\})=0$ simultaneously for all $x\in{\mathbb R}^2$. This  resolves a longstanding open problem posed by S.J. Taylor in 1986.
},
	pages = {no. 15, 1-9},
	issn = {1083-589X},
	doi = {10.1214/ECP.v17-1809},    
        url = {http://ecp.ejpecp.org/article/view/1809}}