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May 8, 2026Open Access

Operator Theory of Distribution Dynamics (OTDD v2.0)

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Authors

LTLászló Tatai

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Overview

This mathematical framework reveals fixed points in probability distributions, suggesting broader applications in statistical dynamics.

Key Points

  • The aim is to establish a mathematical framework where probability distributions behave as fixed points of a nonlinear operator.
  • Introduced a composite nonlinear operator T_θ on probability measures
  • Proved existence of fixed points using the Schauder theorem
  • Derived eigenvalue and spectral gap ratio for a scale-invariant Gamma kernel.
  • Fixed points exemplify various distributions such as power-law and Gaussian
  • Identified a dominant eigenvalue: λ₁(a; κ, β) = β⁻ᵃ · Γ(κ+a) / Γ(κ)
  • Established a critical boundary q = 3/2 ↔ κ = 4 related to GPM–GARCH CLT breakdown.

Cite This Study

László Tatai (2026) studied this question.

synapsesocial.com/papers/69fd7fb8bfa21ec5bbf084f9https://doi.org/10.5281/zenodo.20048351
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