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Renormalization-group theory for finite-size scaling in extreme statistics
G Györgyi1, N R Moloney, K Ozogány
1Department of Theoretical Physics, University of Geneva, Geneva, Switzerland. gyorgyi@glu.elte.hu
Summary
We developed a renormalization-group (RG) approach to understand extreme statistics. This method explains universal patterns in data distributions and calculates corrections for finite-sized datasets.
Area of Science:
- Statistical Physics
- Extreme Value Theory
- Renormalization Group Theory
Background:
- Extreme statistics analyze rare events and tail behaviors of probability distributions.
- Universality in extreme value theory suggests common patterns across different systems.
Purpose of the Study:
- To present a detailed renormalization-group (RG) approach for extreme statistics.
- To explain universal features and finite-size corrections in extreme value distributions.
- To explore similarities between this RG approach and those used in statistical physics.
Main Methods:
- Linearization of the RG transformation near a fixed point.
- Computation of stable perturbations as eigenfunctions.
- Analysis of marginally stable and unstable perturbations.
Main Results:
- Identified fixed points that explain universality in extreme statistics.
- Calculated convergence rates and shape corrections using eigendirections.
- Demonstrated that distributions with unstable perturbations can return to a universal fixed line.
Conclusions:
- The RG approach provides a robust framework for understanding extreme statistics.
- The theory exhibits significant parallels with established RG methods in statistical physics.
- The findings offer insights into the behavior of distribution functions under various perturbations.
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