Exact solution of the master equation for the asymmetric exclusion process

Using the Bethe ansatz, we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one-dimensional lattice. We derive explicit expressions for the conditional probabilities P(x(1),..., x(N); t\y(1),..., y(N); 0) of finding N particles on lattices sites x(1),..., x(N) at time t with initial occupation y(1),..., y(N) at time t = 0.