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I am currently working on a paper and there appears this so called "straightforward estimate": $$\mathbf{P}\{B[0,1] \cap B[3,n] = \emptyset\} \leq \frac{c}{\ln(n)} \quad \text{where}\ c<\infty\ \text{and}\ B\ \text{a 2-dimensional Brownian Motion}. $$ I have to admit that I don't have a clue where this comes from. The worst part is, I don't even have some kind of idea how to approach it. Since it is said to be straightforward I assume it is easy to see though. I don't need a full explanation on how to proof this estimate (not at first at least), I'd rather get some help on the way to do it myself (if it is not harder than it seems to be).

Thanks in advance!

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  • $\begingroup$ Which paper is it from? $\endgroup$ – epimorphic Nov 8 '18 at 18:51
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    $\begingroup$ Gregory Lawler: Hausdorff Dimension of Cut Points for Brownian Motion $\endgroup$ – John Doe Nov 8 '18 at 18:53

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