Relativistic L\'evy processes

TL;DR

This paper introduces relativistic Le9vy processes, a new class of stochastic processes arising from sums of relativistic velocities, with implications for understanding relativistic effects in experiments.

Contribution

It defines and analyzes relativistic Le9vy processes, connecting them to velocity distributions in special relativity and experimental observations.

Findings

Distributions are stable under relativistic velocity addition

Identification of relativistic regimes via distribution concavity

Agreement with heavy-ion diffusion and antiproton cooling data

Abstract

We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a genuinely new class of stochastic processes--relativistic L\'evy processes. Given a system, this allows identifying distinct relativistic regimes in terms of the distribution's concavity at the origin and the probability of measuring relativistic velocities. These features provide a protocol to assess the relevance of stochastic relativistic effects in actual experiments. As supporting evidence, we find agreement with previous results about heavy-ion diffusion and show that our findings are consistent with the distribution of momentum deviations observed in measurements of antiproton cooling.