  This study explores the application of random matrices to track chaotic
dynamics within the Chirikov standard map. Our findings highlight the potential
of matrices exhibiting Wishart-like characteristics, combined with statistical
insights from their eigenvalue density, as a promising avenue for chaos
monitoring. Inspired by a technique originally designed for detecting phase
transitions in spin systems, we successfully adapt and apply it to identify
analogous transformative patterns in the context of the Chirikov standard map.
Leveraging the precision previously demonstrated in localizing critical points
within magnetic systems in our prior research, our method accurately pinpoints
the Chirikov resonance-overlap criterion for the chaos boundary at $K\approx
2.43$, reinforcing its effectiveness.
