Random Walk, Laplace Equation, Poisson Equation, Brownian Motion, Maxwell Boltzmann.
can averaging be justified to give a solution to the Laplace equation at a starting point? In Fig. 1, suppose E_ij be the expectation value of the boundary value reached when starting at the grid point (i, j), due to a random walk property, we can write a relation as follows: The relation (5) is