Density of near-extreme events

Area of Science:

• Statistical Physics
• Extreme Value Theory
• Time Series Analysis

Background:

• Extreme events often cluster, a phenomenon known as crowding.
• Understanding the statistical properties of these clusters is crucial for risk assessment.

Purpose of the Study:

• To quantitatively analyze the crowding of near-extreme events.
• To determine the statistical distributions governing event clustering.

Main Methods:

• Exact computation of the density of states (DOS) near the maximum of random variables.
• Analysis of independent and identically distributed (i.i.d.) random variables.
• Verification for power-law correlated stationary Gaussian sequences.

Main Results:

• The mean DOS converges to three distinct limiting forms based on tail decay rates (slower than exponential, faster than exponential, or pure exponential).
• Theoretical predictions show agreement with real-world data, such as Siberian temperature reconstructions.
• Some findings extend to correlated random variables.

Conclusions:

• The study provides a theoretical framework for understanding extreme event crowding.
• The identified limiting forms offer insights into the statistical behavior of clustered extreme events.
• The findings have implications for modeling and predicting rare but impactful phenomena.