20.500.12556/RUL-179129 Random Lie bracket on $\mathfrak{sl}_2({\mathbf F}_p)$ We study a random walk on the Lie algebra $\mathfrak{sl}_2({\mathbf F}_p)$ where new elements are produced by randomly applying adjoint operators of two generators. Focusing on the generic case where the generators are selected at random, we analyze the limiting distribution of the random walk and the speed at which it converges to this distribution. These questions reduce to the study of a random walk on a cyclic group. We show that, with high probability, the walk exhibits a pre-cutoff phenomenon after roughly $p$ steps. Notably, the limiting distribution need not be uniform, and it depends on the prime divisors of $p-1$. Furthermore, we prove that by incorporating a simple random twist into the walk, we can embed a well-known affine random walk on ${\mathbf F}_p$ into the modified random Lie bracket, allowing us to show that the entire Lie algebra is covered in roughly $\log p$ steps in the generic case. random walks Lie algebras cyclic groups random Lie bracket true false true Angleški jezik Ni določen Članek v reviji 2026-02-05 13:49:46 2026-02-05 13:49:50 2026-02-10 04:26:30 0000-00-00 00:00:00 2026 0 0 19 str. iss. 1, art. e70042 Vol. 68 Jan. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512:519.2 1042-9832 10.1002/rsa.70042 267477251 Random_Struct_Algorithms_-_2026_-_Jezernik_-_Random_Lie_bracket_on_sl2_Fp.pdf Random_Struct_Algorithms_-_2026_-_Jezernik_-_Random_Lie_bracket_on_sl2_Fp.pdf 1 E21CBEC5BC839718290434FABA8A2CA5 ae744993b839c7eb78b70bdfba3885d6a5795d61425c35ac254ad679ef137704 8b2cacc4-05a1-11f1-a1ba-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=227534 https://onlinelibrary.wiley.com/doi/10.1002/rsa.70042 1 10549ce0-0291-11f1-a1ba-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=227324 Fakulteta za matematiko in fiziko 0 0 0