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In this study, considering the Fisher information metric (Fisher metric)given by a specific form, which is the form of weights in statistical physics,we rewrite the Einstein-Hilbert (EH) action. Then, determining thetransformation rules of the Fisher metric, etc under the coarse-graining, weperform the coarse-graining toward that rewritten EH action. We finally show anexistence of a trivial fixed-point. Here, the existence of a trivialfixed-point is not trivial for us because we consider the metric given by theFisher metric, which is not the normal metric and has to satisfy someconstraint in the formalism of the the Fisher metric. We use the path-integralin our analysis. At this time we have to accept that a fundamental constraintin the formalism of the Fisher metric is broken at the quantum level. Howeverwe consider we can accept this with the thought that some constraints andcausal relations held at the classical level usually get broken at the quantumlevel. We finds some problems of the Fisher metric. The space-time we consideris two-dimensional.

Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric