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We consider the fractal percolation process on the unit square with fixed decimation parameterN and level-dependent retention parameters {pk}; that is, for allk ⩾ 1, at thek th stage every retained square of side lengthN1−k is partitioned intoN2 congruent subsquares, and each of these is retained with probabilitypk. independent of all others. We show that if Πkpk =0 (i.e., if the area of the...
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