On Brownian disconnection exponents

Abstract

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.