We derive an upper bound for the disconnection exponent γ of two-dimensional Brownian motion. More precisely, we show that γ≤½-(log2)2/(2π2)<0.47566. This implies in particular that γ is not equal to its trivial upper bound (i.e. ½). We also derive similar estimates of disconnection exponents for several planar Brownian motions and intersection exponents.
"On Brownian disconnection exponents." Bernoulli 1 (4) 371 - 380, December 1995. https://doi.org/10.3150/bj/1193758712