In usual diffusion, the concentration profile, starting from an initial distribution showing sharp features, first gets smooth and then converges to a Gaussian. By considering several examples, we show that the art of convergence to a Gaussian in diffusion in disordered media with infinite contrast may be strikingly different: sharp features of initial distribution do not smooth out at long times. This peculiarity of the strong disorder may be of importance for diagnostics of disorder in complex, e.g., biological, systems.

• Received 19 May 2021
• Revised 28 July 2021
• Accepted 10 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.120601