Fluctuating fronts as correlated extreme value problems: An example of Gaussian statistics

Area of Science:

• Statistical Physics
• Complex Systems
• Reaction-Diffusion Systems

Background:

• Fluctuating particle fronts on lattices can be modeled using extreme value theory.
• Understanding the statistical properties of these fronts is crucial for reaction-diffusion systems.

Purpose of the Study:

• To analyze the extreme value statistics of correlated random variables in fluctuating particle fronts.
• To investigate the probability distribution of the rightmost particle in Fermionic and Bosonic front models.

Main Methods:

• Modeling particle fronts as extreme value problems on a one-dimensional lattice.
• Analyzing the probability distribution P(k(f))(t) for correlated random variables.
• Comparing results from Fermionic and Bosonic front models.

Main Results:

• The probability distribution P(k(f))(t) for the Fermionic front model follows a Gaussian distribution.
• The Bosonic front model shows slight deviations from a Gaussian distribution.

Conclusions:

• The study provides exact results for correlated extreme value statistics in a reaction-diffusion context.
• The distinct behaviors of Fermionic and Bosonic models highlight differences in their statistical properties.