  We study a two-dimensional diffusive motion of a tracer particle in
restricted, crowded anisotropic geometries. The underlying medium is the same
as in our previous work [J. Chem. Phys. 140, 044706 (2014)] in which standard,
gaussian diffusion was studied. Here, a tracer is allowed to perform Cauchy
random walk with uncorrelated steps. Our analysis shows that presence of
obstacles significantly influences motion, which in an obstacle-free space
would be of a superdiffusive type. At the same time, the selfdiffusive process
reveals different anomalous properties, both at the level of a single
trajectory realization and after the ensemble averaging. In particular, due to
obstacles, the sample mean squared displacement asymptotically grows
sublinearly in time, suggesting non-Markov character of motion. Closer
inspection of survival probabilities indicates however that underlying
diffusion is memoryless over long time scales despite strong inhomogeneity of
motion induced by orientational ordering.
