coefficients
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 





R

x
→
y





{\displaystyle \scriptstyle R_{x\rightarrow y}}

 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 




R

x
→
x




{\displaystyle R_{x\rightarrow x}}

 must be −2c. So the probabilities obey the discretized diffusion equation:
