Groupe de Physique Statistique

Equipe 106, Institut Jean Lamour

                     
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Séminaire de groupe

What can we learn from a single trajectory of a stochastic process ?
Alexei Andreanov
MPI Dresden
jeudi 11 avril 2013 , 10h25
Salle de séminaire du groupe de Physique Statistique

We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution.

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