Random Walk, Laplace Equation, Poisson Equation, Brownian Motion, Maxwell Boltzmann.
the steps until the walker exits a boundary point. We then evaluate φ at the exit point of the boundary. This is repeated N times and all the values obtained are averaged. It is known that this average converges to φ(x0, y0) at the rate 1/ sqrt(N). Fig. 1. Coordinate system for the discrete form of