read AppsWZmulti:
#random walk in the square lattice with King's move
L:=[[[1,0],1/8],[[-1,0],1/8],[[0,1],1/8],[[0,-1],1/8],[[1,1],1/8],[[-1,1],1/8],[[1,-1],1/8],[[-1,-1],1/8] ]:
print(`Consider a walk in the square lattice where the `):
print(`distribution of the fundamental steps is`):
print(L):
print(`Let a(n) be the probability of being at the origin after n steps.`):
print(`the probability of returning to the origin after n steps .`):
print(`The linear recurrence operator annihilating a_n:=`):
print(RandomWalkRecurrence(L,n,N));
print(`The whole thing took`, time(), `seconds of CPU time `):
quit: