- #1

davidmoore63@y

- 92

- 17

(a) random walk on a square lattice (step size 1 on the integer lattice for example)

(b) random walk on a triangular lattice (step size 1 on the lattice of equilateral triangles of side 1). Thus there are 6 equiprobable choices for each step in this walk

(c) random walk of step size 1 but with a direction selected from the uniform distribution U[0, 2pi).

My question is, we know that (a) is recurrent (returns to the origin with probability 1). What about (b) and (c) ? Are they recurrent or transient? Intuitively I would say (c) must be transient, but I am struggling with (b).