  It is shown that classical spaces with geometries emerge on boundaries of
randomly connected tensor networks with appropriately chosen tensors in the
thermodynamic limit. With variation of the tensors, the dimensions of the
spaces can be freely chosen, and the geometries, which are curved in general,
can be varied. We give the explicit solvable examples of emergent flat tori in
arbitrary dimensions, and the correspondence from the tensors to the geometries
for general curved cases. The perturbative dynamics in the emergent space is
shown to be described by an effective action which is invariant under the
spatial diffeomorphism due to the underlying orthogonal group symmetry of the
randomly connected tensor network. It is also shown that there are various
phase transitions among spaces, including extended and point-like ones, under
continuous change of the tensors.
