arXiv subjects

Takuya Kaneko

Publications and source records attributed to Takuya Kaneko.

3 recordsLinked to original sources

arXiv2026

Bulk Phase Transition and Edge Behavior in Temporally Correlated Random Matrices

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 $\rho<1$ of the exponential decay correlations; the degenerate limit $\rho\to1^-$ reduces to a symmetrized Volterra operator, connecting to the singular-value cascade identified in a companion BBP analysis. For power-law correlations $dt\sim t^{-\gamma}$, we identify $\gamma_c=1/2$ as the critical point for divergence of the bulk fourth-moment, while $\gamma=1$ marks the breakdown of the flatness condition governing the MDE edge analysis. We prove the fourth-moment transition exactly and find numerically that the self-consistent edge varies smoothly across $\gamma=1$, with no evidence of a kink or discontinuity.

cond-mat.stat-mech↗

arXiv2025

Deformation of semi-circle law for the correlated time series and Phase transition

We study Wigner-type random matrices constructed from financial time series with temporal correlations. We characterize the deformed spectral law through its moments and observe behavior consistent with a modified semicircle law. We apply our framework to several financial time series and observe deviations from the semicircle law in specific foreign exchange markets. The difference from the semicircle law for the financial time series depends on the temporal correlation of financial time series. We provide a moment analysis for both exponential and power law correlation structures and show that the fourth moment increases with the strength of correlations. In the case of power law decay, a transition emerges between regimes with finite and divergent higher-order moments. Finally, numerical simulations support the analytical predictions and reveal finite-size scaling behavior near the transition.

cond-mat.stat-mech↗

arXiv2024

Deformation of Marchenko-Pastur distribution for the correlated time series

We study the eigenvalue of the Wishart matrix, which is created from a time series with temporal correlation. When there is no correlation, the eigenvalue distribution of the Wishart matrix is known as the Marchenko-Pastur distribution (MPD) in the double scaling limit. When there is temporal correlation, the eigenvalue distribution converges to the deformed MPD which has a longer tail and higher peak than the MPD. Here we discuss the moments of distribution and convergence to the deformed MPD for the Gaussian process with a temporal correlation. We show that the second moment increases as the temporal correlation increases. When the temporal correlation is the power decay, we observe a phenomenon such as a phase transition. When $γ>1/2$ which is the power index of the temporal correlation, the second moment of the distribution is finite and the largest eigenvalue is finite. On the other hand, when $γ\leq 1/2$, the second moment is infinite and the largest eigenvalue is infinite. Using finite scaling analysis, we estimate the critical exponent of the phase transition.

cond-mat.stat-mech↗