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On the Poisson distribution of lengths of lattice vectors in a random lattice
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 269, no 3-4, 945-954 p.Article in journal (Refereed) Published
Abstract [en]

We prove that the volumes determined by the lengths of the non-zero vectors +/- x in a random lattice L of covolume 1 define a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real line with intensity 1/2. This generalizes earlier results by Rogers (Proc Lond Math Soc (3) 6:305-320, 1956, Thm. 3) and Schmidt (Acta Math 102: 159-224, 1959, Satz 10).

Place, publisher, year, edition, pages
2011. Vol. 269, no 3-4, 945-954 p.
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URN: urn:nbn:se:uu:diva-132640DOI: 10.1007/s00209-010-0772-8ISI: 000297355500019OAI: oai:DiVA.org:uu-132640DiVA: diva2:358669
Available from: 2010-10-23 Created: 2010-10-23 Last updated: 2012-02-16Bibliographically approved

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