CLT with explicit variance for products of random singular matrices related to Hill’s equation. (English) Zbl 1498.37088
Summary: We prove a central limit theorem (CLT) for the product of a class of random singular matrices related to a random Hill’s equation studied by Adams-Bloch-Lagarias. The CLT features an explicit formula for the variance in terms of the distribution of the matrix entries and this allows for exact calculation in some examples. Our proof relies on a novel connection to the theory of \(m\)-dependent sequences which also leads to an interesting and precise nondegeneracy condition.
MSC:
| 37H15 | Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents |
| 60B20 | Random matrices (probabilistic aspects) |
| 60F05 | Central limit and other weak theorems |
Keywords:
Lyapunov exponent; products of random matrices; central limit theorem; Hill’s equation; \(m\)-dependent sequencesReferences:
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