Spectral content of a single random trajectory
By: Gleb Oshanin
From: U. Pierre et Marie Curie, Paris, France
At: Online - Zoom (https://videoconf-colibri.zoom.us/j/81744277890)
[2020-12-10]
In this presentation I will overview a recent progress in the theoretical, numerical and experimental analyses of spectral densities of individual random trajectories of a finite length. On example of a broad class of anomalous diffusions - the so-called fractional Brownian motion, I will demonstrate that one may calculate analytically the full probability density function of such random functionals, parametrised by a frequency and a finite observation time, and extract a very meaningful information on the evolution of a process under study. In particular, I will show that the large frequency behaviour of the coefficient of variation of this distribution provides a robust criterion of anomalous diffusion, which analytical prediction is validated by a comparison with experiments on dynamics in live cells and in agarose hydrogels, and also by extensive numerical simulations.  If time permits, I will also discuss the peculiarities of spectra in out-of-equilibrium systems, as exemplified by a Brownian Gyrator model, and also of the so-called active Brownian motion.
