  Following our earlier work, we construct statistical discrete geometry by
applying statistical mechanics to discrete (Regge) gravity. We propose a
coarse-graining method for discrete geometry under the assumptions of atomism
and background independence. To maintain these assumptions, restrictions are
given to the theory by introducing cut-offs, both in ultraviolet and infrared
regime. Having a well-defined statistical picture of discrete Regge geometry,
we take the infinite degrees of freedom (large n) limit. We argue that the
correct limit consistent with the restrictions and the background independence
concept is not the continuum limit of statistical mechanics, but the
thermodynamical limit.
