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The aim is to establish finite-step probabilistic bounds for contraction ratios in iterated Pearson correlation dynamics.

Finite-step bounds for iterated correlation matrices

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Randomized analysis establishes upper bounds for contraction ratios in correlation matrices, highlighting implications for convergence dynamics.

The aim is to establish finite-step probabilistic bounds for contraction ratios in iterated Pearson correlation dynamics.
Analyzed contraction ratios represented by ρk = Δk+1/Δk.
Generated sequences using the Pearson correlation update.
Constructed explicit state-dependent bounds based on random initialization of P0.
Finite-step ratios may exceed unity despite Δk converging to 0.
Bounds are induced by independent and identically distributed uniform entries in correlation matrices.
Focused on probabilistic measures for fixed matrix dimensions.

Israa Ali Hassan (2026) studied this question.

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Randomized analysis establishes upper bounds for contraction ratios in correlation matrices, highlighting implications for convergence dynamics.