Krishna B. Athreya

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The two most important notions of fractal dimension are Hausdorff dimension, developed by Hausdorff (1919), and packing dimension, developed independently by Tricot (1982) and Sullivan (1984). Both dimensions have the mathematical advantage of being defined from measures, and both have yielded extensive applications in fractal geometry and dynamical(More)
The two most important notions of fractal dimension are Hausdorff dimension, developed by Hausdorff (1919), and packing dimension, developed independently by Tricot (1982) and Sullivan (1984). Both dimensions have the mathematical advantage of being defined from measures, and both have yielded extensive applications in fractal geometry and dynamical(More)
If qk is the extinction probability of a slightly supercritical branching process with offspring distribution [pkr:r = 0, 1, 2, ...], then it is shown that if supk sigma r r3pkr less than infinity, inf sigma 2k greater than 0, and mk----1, then 1-qk approximately 2(mk - 1)sigma -2k, where mk = sigma r rpkr, sigma 2k = k sigma r r2pkr - m2k. This provides a(More)