Bounds for disconnection exponents (Q1920191)

Let \(B^1,\dots,B^n\) denote \(n\) independent planar Brownian motions started in \((1,0)\). The disconnection exponent is the value \(\eta_n\) such that \(P[\bigcup^n_{j=1} B^j\) does not disconnect \(0\) from infinity] is logarithmically equivalent to \(t^{-\eta_n/2}\) for \(t\to\infty\). The main purpose of the paper is to improve the upper bounds for \(\eta_n\) derived by the author [Bernoulli 1, No. 4, 371-380 (1995; Zbl 0845.60083)]. In addition, a proof of the lower bound \(1/2\pi\) for \(\eta_1\) is given.