Hello all,

I want to prove that any flow on the following tree must have an infinite energy.

The structure of the graph is (taken from R.Lyons and Y.Peres book)

"We’ll construct a tree $T$ embedded in the upper half plane with o at the origin. We’ll have $|T_n| = 2^n$, but we’ll connect them in a funny way. List $T_n$ in clockwise order as $(x^n_1 , . . . , x^n_{2^n})$. Let $x^n_k$ have $1$ child if $k \leq 2^{n−1}$ and $3$ children otherwise."

Any idea?

Thanks in advance!