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Bounds for disconnection exponents. (English) Zbl 0862.60069

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.

MSC:

60J65 Brownian motion

Citations:

Zbl 0845.60083
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