What does this research mean for the field?

The Brody distribution's information geometry reveals that the effective statistical dimension of nearest-neighbor spacings in β-ensembles is d_eff = (β+2)/β, with significant implications for understanding quantum spectral fluctuations and chaos compression. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to explore the information geometry of the Brody distribution, focusing on its Fisher metric and effective dimensions.

March 7, 2026Open Access

Information Geometry of the Brody Distribution: Exact Fisher Metric, Effective Dimension, and Spectral Duality

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Authors

JWJon Wiberg

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Implication

Demonstrates exact relationships in the Brody distribution's information geometry, indicating implications for quantum chaos analysis.

Key Points

The aim is to explore the information geometry of the Brody distribution, focusing on its Fisher metric and effective dimensions.
Derived the Fisher-Rao metric on the Brody manifold in closed form.
Investigated the Amari α-connection structure and its implications for statistical families.
Proved the effective statistical dimension and spectral duality theorems through various approaches.
Established that the effective dimension of nearest-neighbor spacings is d_eff = (β+2)/β.
Discovered a relationship between the Weibull dimension and effective dimension (d_W − 1)(d_eff − 1) = 2.
Showed that variance excess ε(β) is linear in d_eff, providing a connection between spectral data and effective dimension.

Cite This Study

Jon Wiberg (2026) studied this question.

synapsesocial.com/papers/69abc2615af8044f7a4ebe83 https://doi.org/10.5281/zenodo.18879755

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Information Geometry of the Brody Distribution: Exact Fisher Metric, Effective Dimension, and Spectral Duality

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Key Points

Cite This Study

Information Geometry of the Brody Distribution: Exact Fisher Metric, Effective Dimension, and Spectral Duality

Discussion

Member takes

Implication

Key Points

Cite This Study

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