Hausdorff dimension of limsup random fractals
نویسنده
چکیده
In this paper we find a critical condition for nonempty intersection of a limsup random fractal and an independent fractal percolation set defined on the boundary of a spherically symmetric tree. We then use a codimension argument to derive a formula for the Hausdorff dimension of limsup random fractals.
منابع مشابه
Limsup Random Fractals
Orey and Taylor (1974) introduced sets of “fast points” where Brownian increments are exceptionally large, F(λ) := {t ∈ [0, 1] : lim suph→0 |X(t+ h) −X(t)|/ √ 2h| log h|>λ}. They proved that for λ ∈ (0, 1], the Hausdorff dimension of F(λ) is 1 − λ2 a.s. We prove that for any analytic set E ⊂ [0, 1], the supremum of all λ’s for which E intersects F(λ) a.s. equals √ dimP E, where dimP E is the pa...
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