The process with parameters p , q ⩾ ⩾ 0 , p + q = 1 is a continuous-time Markov process on S = { 0 , 1 } Z , the 1s being thought of as particles and the 0s as empty sites. Each particle waits a random amount of time having the distribution of an exponential random variable with mean one and then attempts a jump, one site to the right with probability p and one site to the left with probability q . However, the jump is performed only if there is no particle at the target site. Otherwise, nothing happens and the particle waits another exponential time. All particles are doing this independently of each other.