Edgeworth Expansion and Large Deviations for the Coefficients of Products of Positive Random Matrices

• Published in: Journal of theoretical probability Vol. 38; no. 2
• Main Authors: Xiao, Hui, Grama, Ion, Liu, Quansheng
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2025; Springer Nature B.V
• Subjects: Deviation; Mathematics; Mathematics and Statistics; Probability Theory and Stochastic Processes; Statistics; Theorems; Berry–Esseen theorem; Primary 60F05; Spectral gap; 60F10; Edgeworth expansion; Precise large deviations; Secondary 60J05; 60B20; Products of positive random matrices; Local limit theorem

Consider the matrix products G n : = g n ⋯ g 1 , where ( g n ) n ⩾ 1 is a sequence of independent and identically distributed positive random d × d matrices. Under the optimal third moment condition, we first establish a Berry–Esseen theorem and an Edgeworth expansion for the ( i ,  j )-th entry G n...