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Hausdorff Dimension of Cut Points for Brownian Motion

   
@article{EJP2,
	author = {Gregory Lawler},
	title = {Hausdorff Dimension of Cut Points for Brownian Motion},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {1},
	year = {1995},
	keywords = {Brownian motion,Hausdorff dimension, cut points, intersection exponent},
	abstract = {Let $B$ be a Brownian motion in $R^d$, $d=2,3$. A time $t\in [0,1]$ is called a cut time for $B[0,1]$ if $B[0,t) \cap B(t,1] = \emptyset$. We show that the Hausdorff dimension of the set of cut times equals $1 - \zeta$, where $\zeta = \zeta_d$ is the intersection exponent. The theorem, combined with known estimates on $\zeta_3$, shows that the percolation dimension of Brownian motion (the minimal Hausdorff dimension of a subpath of a Brownian path) is strictly greater than one in $R^3$.},
	pages = {no. 2, 1-20},
	issn = {1083-6489},
	doi = {10.1214/EJP.v1-2},    
        url = {http://ejp.ejpecp.org/article/view/2}}