The triangle law for Lyapunov exponents of large random matrices

Marco Isopi; Charles M. Newman

doi:10.1007/BF02099267

The triangle law for Lyapunov exponents of large random matrices

Marco Isopi, Charles M. Newman

Mathematics

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

Abstract

For products, A(t)·A(t-1)... A(1), of i.i.d. N×N random matrices, with i.i.d. entries, a triangle law governs the N→∞ distribution of Lyapunov exponents, much like Wigner's quarter-circle law governs the singular values of A(1). Our proof requires finite fourth moments and a bounded density; the result was previously derived only in the Gaussian case.

Original language	English (US)
Pages (from-to)	591-598
Number of pages	8
Journal	Communications In Mathematical Physics
Volume	143
Issue number	3
DOIs	https://doi.org/10.1007/BF02099267
State	Published - Jan 1992

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02099267

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title = "The triangle law for Lyapunov exponents of large random matrices",

abstract = "For products, A(t)·A(t-1)... A(1), of i.i.d. N×N random matrices, with i.i.d. entries, a triangle law governs the N→∞ distribution of Lyapunov exponents, much like Wigner's quarter-circle law governs the singular values of A(1). Our proof requires finite fourth moments and a bounded density; the result was previously derived only in the Gaussian case.",

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AB - For products, A(t)·A(t-1)... A(1), of i.i.d. N×N random matrices, with i.i.d. entries, a triangle law governs the N→∞ distribution of Lyapunov exponents, much like Wigner's quarter-circle law governs the singular values of A(1). Our proof requires finite fourth moments and a bounded density; the result was previously derived only in the Gaussian case.

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The triangle law for Lyapunov exponents of large random matrices

Abstract

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