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?