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arXiv · 2412.18581

Relativistic L\'evy processes

Lucas G. B. de Souza·M. G. E. da Luz·E. P. Raposo·Evaldo M. F. Curado·G. M. Viswanathan
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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.

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Lucas G. B. de Souza, M. G. E. da Luz, E. P. Raposo, Evaldo M. F. Curado, G. M. Viswanathan. 2024-12-24. Relativistic L\'evy processes. https://doi.org/10.1103/wf2s-g7lv

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