Spectral Construction of Optimal Weighted Wasserstein Metrics for Random Logistic-Type Maps

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Key Points

The aim is to develop a spectral construction for optimal weighted Wasserstein metrics in the context of random logistic-type maps.
Defined conditions for weighted contractions using Lyapunov exponents.
Replaced ad hoc weight constructions with spectral theory for a derivative transfer operator.
Analyzed optimal contraction constants across continuous weight functions.
Established a relationship between the optimal contraction constant and the spectral radius of the derivative transfer operator.
Showed that the associated Markov operator is a strict contraction in a weighted Wasserstein metric.
Demonstrated that positive weights can ensure contractive behavior even under negative Lyapunov exponents.

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Investigates spectral construction of optimal metrics in one-dimensional maps, suggesting improved contraction under weighted conditions.

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Ramen Ghosh (2026) studied this question.

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