Implementation of finite-step bounds shows contraction behavior in dynamics, indicating reliable predictive measures.
R code implementing finite-step probabilistic upper bounds for iterated Pearson correlation dynamics. From uniform [-1,1] initialization, constructs state-dependent functions controlling contraction ratios conditional on normalized step size. Implements conditional quantile bounds via logarithmic binning, deterministic enlargement families, and out-of-sample validation. Computes expansion thresholds below which contraction is guaranteed with a given probability, and worst-case envelope bounds. Includes replication scripts for all figures and tables. Validated for matrix dimensions three to two thousand.
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Ishrak Alhajj Hassan (2026) studied this question.
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