Before revision:  Markovian tasks can be characterised by a state space and a transition matrix . In mammals, the firing of populations of place or grid cells in the hippocampal formation are thought to represent the probability distribution over state space. Grid firing patterns are suggested to be eigenvectors of a transition matrix reflecting diffusion across states, allowing simple prediction of future state distributions , by replacing matrix multiplication with elementwise multiplication by eigenvalues .
After revision:  Markovian tasks can be characterised by a state space and a transition matrix and recent work has proposed that neural grid codes provide an efficient representation of the state space, as eigenvectors of a transition matrix reflecting diffusion across states, allowing simple prediction of future state distributions , by replacing matrix multiplication with elementwise multiplication by eigenvalues .