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- W14976978 abstract "Motivated by a question of Mandelbrot [4, Chapter 25], Mountford [5] has investigated the properties of the connected components of the complement of a two-dimensional Brownian path. Let (B = left( {{B_t},t geqslant 0} right)) be a Brownian motion in the complex plane ℂ, and (Bleft[ {0,1} right] = left{ {{B_t},0 leqslant t leqslant 1} right}) For any u, y with (0 < mu < upsilon leqslant infty), let N [u,υ) denote the number of connected components of ℂB[0, 1] with area in [u, υ). Mountford [5] has proved that for every λ ∈ (0, 1), $${x^2}{left( {log x} right)^2}Nleft( {pi {{left( {lambda chi } right)}^2},pi {chi ^2}} right)xrightarrow[{x to 0}]{{left( {Pr obability} right)}}frac{1}{2}left( {{lambda ^{ - 2}} - 1} right)$$(1.a)" @default.
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- W14976978 date "1991-01-01" @default.
- W14976978 modified "2023-09-23" @default.
- W14976978 title "On the Connected Components of the Complement of a Two-Dimensional Brownian Path" @default.
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- W14976978 doi "https://doi.org/10.1007/978-1-4612-0459-6_18" @default.
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