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Moritz Jirak 《Journal of multivariate analysis》2011,102(6):1032-1046
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Special Transverse Slices and Their Enveloping Algebras 总被引:1,自引:0,他引:1
Alexander Premet 《Advances in Mathematics》2002,170(1):1-55
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Consider the Dvoretzky random covering on the circle T with a decreasing length sequence {?n}n?1 such that . We study, for a given β?0, the set Fβ of points which are asymptotically covered by a number βLn of the first n randomly placed intervals where . Three typical situations arise, delimited by two “phase transitions”, according to is zero, positive-finite or infinite, where . More precisely, if ?n tends to zero rapidly enough so that then, with probability one, dimHFβ=1 for all β?0; if ?n is moderate so that then, with probability one, we have for and Fβ=∅ for where and is the interval consisting of β's such that ; eventually, if ?n is so slow that then, with probability one, F1=T. This solves a problem raised by L. Carleson in a rather satisfactory fashion.Analogous results are obtained for the Poisson covering of the line, which is studied as a tool. 相似文献