Local limit theorem for the operator norm of products of random matrices

2026/07/22 by Ion Grama, Jean-François Quint, Hui Xiao · 1 citation
Mathematics · #math.GR #math.PR #msc:22D40 #msc:22E46 #msc:60F05 #msc:60J05 #msc:60J10.

paper · pdf

63 pages, 1 figure, a few misprints corrected

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We prove a local limit theorem for the quantity ‖ g_n ⋯ g₁ ‖, where g₁, g₂, … is a sequence of independent and identically distributed random invertible square matrices. The norm ‖ ⋅ ‖ is arbitrary and we make no proximality assumption.

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