TITLE: How many proofs of the Polya's recurrent theorem are there?
QUESTION [11 upvotes]: Polya's  famous theorem states that a simple random walk on $\mathbb{Z}^d$ is transient if $d>2$ and recurrent if $d=1,2$. This theorem is included in almost every textbook on probability theory.
As far as I know there are four proofs:

By a pure combinatorial enumeration of the walks that return to the starting point via stirling' formula.
A Fourier transformation computation of the Green function $G(x,y)=\sum_nP_x(S_n=y)$.
Foster-Lyapunov criterion for recurrent and transient.
By Lyons's theorem, construct an unit flow of finite energy from origin to infinity .

My question is , are there more proofs?

REPLY [3 votes]: It is amusing that a unit flow of finite energy in the $d$-dimensional lattice for $d \ge 3$ can be easily constructed from Polya's urn; see 
``Polya's theorem on random walks via Polya's urn'',  Amer. Math. Monthly 117 (2010), no. 3, 220–231.