Consider a restricted 2d random walk the random on a square lattice with lattice constant a walker is not allowed to step back, but it ca go forward, turn right and turn left with can 1 equal probability. calculate the mean-square end-to-end distance for such a restricted n-step random walk starting with the general equation n n 2(cos (0)) r2) (3) = a i=1 j=1 which in this case can be evaluated analytically. note that the values for the cosines can be only 0, 1 or - on the square lattice. derive the exact result for the characteristic ratio cn.