Abstract
Let Wt be Brownian motion in the plane started at the origin and let θ be the first exit time of the unit disk D1. Let μθ(x,ϵ)=1 πϵ2 ∫0θ1 {B(x,ϵ)}(Wt)dt, and set μθ∗(ϵ)=supx∈D1μθ(x,ϵ). We show that μθ∗(ϵ)− 2∕πlogϵ−1−1 2loglogϵ−1 is tight.
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