Fig. 1

Schematic of the probabilistic model. a a typical distribution of particles at t + Δt (thick circles) with an indication of the position of a representative particle at t (dashed circle). b the case where the nearest particle is the original particle. c the case where the nearest particle is a surrounding particle. Gray color indicates the identification of the original particle. The large dotted circles indicate the distance to the nearest particle. The distance to the nearest neighbor of the origin at the subsequent time frame is modeled by the probabilistic model with respect to the diffusion constant of the original particle and the particle density at the origin