Bulk Phase Transition and Edge Behavior in Temporally Correlated Random Matrices

Masato Hisakado and Takuya Kaneko

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Abstract: We study long-range correlated Wigner-type matrices built from row-independent stationary Gaussian sequences. For exponentially decaying (AR(1)) correlations, the bulk spectral density deforms from the semicircle law via an explicit combinatorial "hub" mechanism, yet we verify the flatness and decay hypotheses of the matrix-Dyson-equation framework (MDE), with numerical evidence supporting Tracy-Widom edge universality for every fixed $\rho

Date: 2026-08
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