On the Green's function for a one-dimensional random walk.
The Green's function of a random walk on a lattice is defined as the inverse of the operator K - z1, where K is the matrix of transition rates and z is an arbitrary complex parameter. The Green's function for a symmetrical random walk in one dimension is here explicitly given in closed form for reflecting, periodic, and absorbing boundaries, and also for an infinite lattice.
D055592:Biophysical Phenomena; D001703:Biophysics; D003461:Crystallography; D011336:Probability; D013269:Stochastic Processes