caa a22 4500 445836733 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0772-8 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0772-8 Södergren Anders Department of Mathematics, Uppsala University, Box 480, 75106, Uppsala, Sweden aut On the Poisson distribution of lengths of lattice vectors in a random lattice [Elektronische Daten] [Anders Södergren] 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 $${\frac{1}{2}}$$ . 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). Springer-Verlag, 2010 Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 945-954 0025-5874 269:3-4<945 2011 269 209 https://doi.org/10.1007/s00209-010-0772-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0772-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Södergren Anders Department of Mathematics, Uppsala University, Box 480, 75106, Uppsala, Sweden aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 945-954 0025-5874 269:3-4<945 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer