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    Cut points on Brownian paths 

    Burdzy, Krzysztof (Institute of Mathematical Statistics, 1989-07)
    Let X be a standard two-dimensional Brownian motion. There exists a.s. t [is an element of the set] (0; 1) such that X([0; t))[intersected with] X((t; 1]) = [empty set]. It follows that X([0; 1]) is not homeomorphic to the Sierpinski carpet a.s.
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    Non-intersection exponents for Brownian paths. Part II: Estimations and applications to a random fractal. 

    Burdzy, Krzysztof; Lawler, Gregory F. (Institute of Mathematical Statistics, 1990-07)
    Let X and Y be independent two-dimensional Brownian motions, X(0) = (0; 0); Y(0) = ([epsilon]; 0), and let p([epsilon]) = P(X[0; 1] [intersected with] Y [0; 1] = [empty set], q([epsilon]) = {Y [0; 1] does not contain a closed loop around 0}. Asymptotic estimates (when [epsilon] --> 0) of p([epsilon]); q([epsilon]), and some ...
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    Labyrinth dimension of Brownian trace 

    Burdzy, Krzysztof (Institute of Mathematics, 1995)
    Suppose that X is a two-dimensional Brownian motion. The trace X[0, 1] contains a self-avoiding continuous path whose Hausdorff dimension is equal to 2.

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    Author
    Burdzy, Krzysztof (3)
    Lawler, Gregory F. (1)Subject
    Brownian motion (3)
    fractal (3)
    critical exponents (1)cut point (1)cut points (1)Hausdorff dimension (1)intersections of Brownian paths (1)random fractal (1)... View MoreDate Issued1995 (1)1990 (1)1989 (1)

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