Abstract
In Chapter 15 we consider matchings in dimension ≥3. We are able to obtain the seemingly final result, a strong version of “the ultimate matching conjecture”. There are no more fractional powers of logN here, but in a random sample of N points uniformly distributed in [0,1]3, local irregularities occur at all scales between N −1/3 and (logN)1/3 N −1/3, and our result can be seen as a precise global description of these irregularities.
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References
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Talagrand, M. (2014). The Ultimate Matching Theorem in Dimension ≥3. In: Upper and Lower Bounds for Stochastic Processes. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54075-2_15
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DOI: https://doi.org/10.1007/978-3-642-54075-2_15
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