Abstract
We show how a Brownian motion on a short scale can originate a relativistic motion on scales larger than particle's Compton wavelength. Special relativity appears to be not a primitive concept, but rather it statistically emerges when a coarse graining average over distances of order, or longer than the Compton wavelength is taken. Our scheme accommodates easily also the doubly special relativistic dynamics. A previously unsuspected, common statistical origin of the two frameworks is brought to light for the first time.
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