科研之友
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摘要
We pursue the analysis made in Desbois and Ouvry (2011 J. Stat. Mech. P05024) on the arithmetic area enclosed by m closed Brownian paths. We pay particular attention to the random variable S-n1,S-n2,S-...,S-nm (m), which is the arithmetic area of the set of points, also called winding sectors, enclosed n(1) times by path 1, n(2) times by path 2,..., and n(m) times by path m. Various results are obtained in the asymptotic limit m -> infinity. A key observation is that, since the paths are independent, one can use in the m-path case the SLE information, valid in the one-path case, on the zero-winding sectors arithmetic area.
- 出版日期2012-5
