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Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices
- Publication Year :
- 2020
-
Abstract
- Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed positive random $d\times d$ matrices and consider the matrix product $G_n: = g_n \ldots g_1$. Under suitable conditions, we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and moderate deviation expansions of Cram\'er type, for the matrix norm $\| G_n \|$ of $G_n$, for its $(i,j)$-th entry $G_n^{i,j}$, and the and for its spectral radius $\rho(G_n)$.
- Subjects :
- Mathematics - Probability
Primary 60F05, 60F10, 60B20, Secondary 60J05, 60B15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2010.00557
- Document Type :
- Working Paper