The second quantity is known as the correlation function. The delta is the kronecker delta which tells us that if the indices i and j are different, then the result is 0, but if i = j then the kronecker delta is 1, so the correlation function returns a value of b. This makes sense, because if i = j then we are considering the same step. Rather trivially then it can be shown that the average displacement of the train on the x-axis is 0;