Products of random matrices: Dimension and growth in norm

Vladislav Kargin

doi:10.1214/09-AAP658

Products of random matrices: Dimension and growth in norm

Vladislav Kargin

Mathematics and Statistics

Binghamton University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Suppose that X₁, ...,X_n, ... are i.i.d. rotationally invariant N-by-N matrices. Let ∏_n = X_n X₁. It is known that n^-1 log | ∏_n | converges to a non-random limit. We prove that under certain additional assumptions on matrices X_i the speed of convergence to this limit does not decrease when the size of matrices, N, grows.

Original language	English
Pages (from-to)	890-906
Number of pages	17
Journal	Annals of Applied Probability
Volume	20
Issue number	3
DOIs	https://doi.org/10.1214/09-AAP658
State	Published - Jun 2010

Keywords

Furstenberg-Kesten theorem
Random matrices

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title = "Products of random matrices: Dimension and growth in norm",

abstract = "Suppose that X1, ...,Xn, ... are i.i.d. rotationally invariant N-by-N matrices. Let ∏n = Xn X1. It is known that n-1 log | ∏n | converges to a non-random limit. We prove that under certain additional assumptions on matrices Xi the speed of convergence to this limit does not decrease when the size of matrices, N, grows.",

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N2 - Suppose that X1, ...,Xn, ... are i.i.d. rotationally invariant N-by-N matrices. Let ∏n = Xn X1. It is known that n-1 log | ∏n | converges to a non-random limit. We prove that under certain additional assumptions on matrices Xi the speed of convergence to this limit does not decrease when the size of matrices, N, grows.

AB - Suppose that X1, ...,Xn, ... are i.i.d. rotationally invariant N-by-N matrices. Let ∏n = Xn X1. It is known that n-1 log | ∏n | converges to a non-random limit. We prove that under certain additional assumptions on matrices Xi the speed of convergence to this limit does not decrease when the size of matrices, N, grows.

KW - Furstenberg-Kesten theorem

KW - Random matrices

UR - https://www.scopus.com/pages/publications/77953850098

U2 - 10.1214/09-AAP658

DO - 10.1214/09-AAP658

M3 - Article

SN - 1050-5164

VL - 20

SP - 890

EP - 906

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 3

ER -

Products of random matrices: Dimension and growth in norm

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Keywords

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