  Logarithmic potentials and many other potentials satisfy maximum principle.
The dyadic version of logarithmic potential can be easily introduced, it lives
on dyadic tree and also satisfies maximum principle. But its analog on bi-tree
does not have this property. We prove here that "on average" we can still have
something like maximum principle on bi-tree. We use the surrogate maximum
principle to prove embedding theorems of Carleson type on bi-disc.
