Nonintersecting planar Brownian motions.
Nonintersecting planar Brownian motions.
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非相交平面布朗运动。
DOI：
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发表时间：
1995
期刊：
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通讯作者：
G. Lawler
中科院分区：
文献类型：
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作者：
G. Lawler
在这篇文章中，我们构造了一种关于始于同一点的布朗运动对的度量，条件是它们的路径不相交。这一度量的构造是将不相交的布朗运动严格理解为共形区域的一个开始。设B1；B2是R2中始于单位圆上不同点的独立布朗运动。设Tj r是第j次布朗运动到达距离r的第一次时间，Dr是事件Dr=FB1 0；T1 er]B2 0；T2 er]=；g：我们通过考虑以事件Dr为条件的Brown运动诱导的测度的极限来构造测度.
In this paper we construct a measure on pairs of Brownian motions starting at the same point conditioned so their paths do not intersect. The construction of this measure is a start towards the rigorous understanding of nonintersecting Brownian motions as a conformal eld. Let B 1 ; B 2 be independent Brownian motions in R 2 starting at distinct points on the unit circle. Let T j r be the rst time that the jth Brownian motion reaches distance r and let D r be the event D r = fB 1 0; T 1 e r ] B 2 0; T 2 e r ] = ;g: We construct the measure by considering the limit of the measure induced by Brownian motions conditioned on the event D r .