Projections of the natural measure for percolation fractals

We prove that, with probability 1, all orthogonal projections of the natural measure on a percolation fractal are absolutely continuous and (except for the horizontal and vertical projection) have H¨older continuous density.

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 214; no. 2; pp. 539 - 552
Main Authors Peres, Yuval, Rams, Michał
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.07.2016
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Fractals
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Percolation
Theoretical
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Summary:We prove that, with probability 1, all orthogonal projections of the natural measure on a percolation fractal are absolutely continuous and (except for the horizontal and vertical projection) have H¨older continuous density.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1343-4