Finite free perpetuities are defined as degree-n monic polynomials solving a truncated perpetuity equation; the paper proves existence, uniqueness, real nonnegative zeros for admissible (A,B), and weak convergence of root distributions to free perpetuity laws.
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Matrix perpetuities under orthogonal invariance have power-law tailed expected empirical spectral distributions governed by the largest eigenvalue, with high-dimensional limits given by free perpetuities in the subcritical regime.
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Finite free perpetuities
Finite free perpetuities are defined as degree-n monic polynomials solving a truncated perpetuity equation; the paper proves existence, uniqueness, real nonnegative zeros for admissible (A,B), and weak convergence of root distributions to free perpetuity laws.
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On the empirical spectral distribution of matrix perpetuities
Matrix perpetuities under orthogonal invariance have power-law tailed expected empirical spectral distributions governed by the largest eigenvalue, with high-dimensional limits given by free perpetuities in the subcritical regime.