Figure 2.

Random walk and random walk with drift. (A) Shown is the particle density for a nonuniform one-dimensional random walk over time (with probability higher to the right side of the space). (B) Shown are the eigenvalues for the nonuniform one-dimensional random walk. The eigenvalues at the first step of the simulation are not at unity contrary to the uniform random walk. (C) At the first step of the simulation for the one-dimensional random walk, the eigenvalue is equal to the squared rate given for the nonuniform simulation. This result is universal for any rates given. (D) The eigenvalues at the first step of a uniform simulation are also equal to the squared rate of the simulation, i.e., squared of one over the number of parameters. To see this figure in color, go online.