For a particle described by probability theory random walking on a line, the analogous thing is the list of probabilities ( … … , P − − 2 , P − − 1 , P 0 , P 1 , P 2 , … … ) , which give the probability of any position. The quantities that describe how they change in time are the transition probabilities K x → → y ( t ) , which gives the probability that, starting at x, the particle ends up at y time t later. The total probability of ending up at y is given by the sum over all the possibilities