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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Poissonian renormalizations, exponentials, and power laws.
1Holon Institute of Technology, P.O. Box 305, Holon 58102, Israel. eliazar@post.tau.ac.il
Summary
This study explores Poisson processes and their link to extreme value laws using renormalization. It reveals how these processes explain the widespread occurrence of white and 1/f noise.
Area of Science:
- Statistical Physics
- Probability Theory
Background:
- Poisson processes are fundamental to extreme value laws (Gumbel, Fréchet, Weibull).
- Understanding their dynamics is crucial for various scientific fields.
Purpose of the Study:
- To conduct a comprehensive renormalization study of Poisson processes.
- To analyze the emergence, dynamics, and phase transitions of these processes.
- To establish a Poissonian explanation for the ubiquity of white and 1/f noise.
Main Methods:
- Application of the Poissonian renormalization method.
- Analysis of exponential and power-law intensity distributions.
- Characterization of structural phase transitions.
Main Results:
- Unveiled intrinsic dynamical structures of Poisson processes.
- Determined domains of attraction for these processes.
- Identified connections between structural phase transitions, uniform/harmonic intensities, and noise phenomena.
Conclusions:
- Poissonian renormalization provides a framework for understanding extreme value laws.
- The study establishes a novel explanation for the prevalence of white and 1/f noise.
- Demonstrated universal properties of structural phase transitions in these systems.
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