Assuming that the trajectory of a single particle measured at time points 1 Δ Δ t , 2 Δ Δ t , … … , N Δ Δ t , where Δ Δ t is any fixed number, then there are N ( N − − 1 ) / 2 non-trivial forward displacements d → → i j = r → → j − − r → → i ( 1 ⩽ ⩽ i < j ⩽ ⩽ N , the cases when i = j are not considered) which correspond to time intervals (or time lags) Δ Δ t i j = ( j − − i ) Δ Δ t . Hence, there are many distinct displacements for small time lags, and very few for large time lags, M S D can be defined as an average quantity over time lags: