Speaker
Yann Lanoiselée
(PMC lab - École Polytechnique)
Description
Recent progresses in single particle tracking have shown evidences of
non-Gaussian distribution of displacements in biological media either
near the cellular membrane or inside the cytoskeleton. A similar
behavior has also been reported in granular media, turbulent flows,
gels, colloidal suspensions. Its emergence in various fields suggests
that this is a general feature of diffusion in complex media. A possible
interpretation of this phenomenon is that tracers experience a medium
with spatio-temporal fluctuations which result in local changes of
diffusivity. We propose and investigate an ergodic easily interpretable
model, which is based on diffusing diffusivity. Depending on the
parameters, the displacement distribution can exhibit either a pure
exponential shape, or a Gaussian-like behavior at small displacements
with an exponential tail at large displacements, or be reduced to a
purely Gaussian one in the Brownian limit. We show that the distribution
converges to a Gaussian one slowly, as 1/t. We calculate relevant
statistical properties and propose steps to estimate the model
parameters from a sufficiently long single trajectory.
Primary author
Yann Lanoiselée
(PMC lab - École Polytechnique)
Co-author
Denis Grebenkov
(CNRS)
