One simple case to study is when the R matrix has an equal probability to go one unit to the left or to the right, describing a particle that has a constant rate of random walking. In this case formula_45 is zero unless y is either "x" + 1, "x", or "x" − 1, when "y" is "x" + 1 or "x" − 1, the "R" matrix has value "c", and in order for the sum of the "R" matrix coefficients to equal zero, the value of formula_50 must be −2"c". So the probabilities obey the discretized diffusion equation: