Relativistic Lévy processes

Area of Science:

• Physics
• Mathematics
• Statistical Mechanics

Background:

• Stochastic processes are fundamental in physics.
• Special relativity governs high-velocity phenomena.
• Understanding random velocity distributions is key in relativistic systems.

Purpose of the Study:

• To investigate sums of independent and identically distributed random velocities in special relativity.
• To introduce and characterize a new class of stochastic processes: relativistic Lévy processes.
• To develop a method for identifying relativistic regimes and assessing stochastic relativistic effects.

Main Methods:

• Mathematical analysis of velocity distributions under relativistic velocity addition.
• Characterization of the new processes based on distribution concavity and measurement probabilities.
• Comparison with experimental data from heavy-ion diffusion and antiproton cooling.

Main Results:

• The one-dimensional velocity distributions are stable under relativistic velocity addition.
• A new class of stochastic processes, relativistic Lévy processes, has been defined.
• Relativistic regimes can be identified by distribution concavity and measurement probabilities.
• Findings align with heavy-ion diffusion and antiproton cooling momentum deviations.

Conclusions:

• Relativistic Lévy processes represent a novel framework for stochastic phenomena in special relativity.
• The study provides a protocol to evaluate the significance of relativistic stochastic effects in experiments.
• The results offer insights into particle behavior in high-energy physics and accelerator experiments.