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Where does randomness lead in spacetime?

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It is well known that particles move in straight lines in space time in absence of any field: these are the geodesics of Minkowski spacetime. There is essentially a unique way to perturb randomly this motion in a physical way, giving raise to the ‘relativistic diffusion’. What eventually happens to this object? I will explain how different points of view can lead to an explicit and complete answer to this question. Couplings of SDEs, random walks on groups and (a bit of) conformal geometry will enter the scene.

This talk is part of the Probability series.

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