20.500.12556/RUL-175454 A completion of counterexamples to the classical central limit theorem for triplewise independent and identically distributed random variables By the Lindeberg–Lévy central limit theorem, standardized partial sums of a sequence of mutually independent and identically distributed random variables converge in law to the standard normal distribution. It is known that mutual independence cannot be relaxed to pairwise independence, nor even to triplewise independence. Counterexamples have been constructed for most marginal distributions: a recent construction works under a condition which excludes certain probability distributions with atomic parts, in particular almost all distributions on a fixed finite set. In the present paper, we show that this condition can be lifted: for any probability distribution ▫$F$▫ on the real line, which has finite variance and is not concentrated in a single point, there exists a sequence of triplewise independent random variables with distribution ▫$F$▫, such that its standardized partial sums converge in law to a distribution which is not normal. There is also scope for extension to ▫$k$▫-tuplewise independence. central limit theorem mutual independence triplewise independence centralni limitni izrek vzajemna neodvisnost neodvisnost po trojicah true false true Angleški jezik Slovenski jezik Članek v reviji 2025-10-28 09:34:17 2025-10-28 09:34:21 2026-06-30 10:58:15 0000-00-00 00:00:00 2025 0 0 5 str. art. 110508 Vol. 226 Nov. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 0167-7152 10.1016/j.spl.2025.110508 245761283 1-s2.0-S0167715225001531-main-2.pdf 1-s2.0-S0167715225001531-main-2.pdf 1 0D49FF03FD3AC1E568871F949B0EE2B6 5fc940f455e31a4965c18a954ad05441cfc6e7261b92689c38ae06e3d360441c fd1ed51a-b3d8-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=221005 https://www.sciencedirect.com/science/article/pii/S0167715225001531 1 9a2d732e-b3d8-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=221004 Fakulteta za matematiko in fiziko 0 0 0