2022
DOI: 10.1017/jpr.2022.53
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Time-convergent random matrices from mean-field pinned interacting eigenvalues

Abstract: We study a multivariate system over a finite lifespan represented by a Hermitian-valued random matrix process whose eigenvalues (i) interact in a mean-field way and (ii) converge to their weighted ensemble average at their terminal time. We prove that such a system is guaranteed to converge in time to the identity matrix that is scaled by a Gaussian random variable whose variance is inversely proportional to the dimension of the matrix. As the size of the system grows asymptotically, the eigenvalues tend to mu… Show more

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