  We develop a method for evaluating restricted isometry constants (RICs). This
evaluation is reduced to the identification of the zero-points of entropy,
which is defined for submatrices that are composed of columns selected from a
given measurement matrix. Using the replica method developed in statistical
mechanics, we assess RICs for Gaussian random matrices under the replica
symmetric (RS) assumption. In order to numerically validate the adequacy of our
analysis, we employ the exchange Monte Carlo (EMC) method, which has been
empirically demonstrated to achieve much higher numerical accuracy than naive
Monte Carlo methods. The EMC method suggests that our theoretical estimation of
an RIC corresponds to an upper bound that is tighter than in preceding studies.
Physical consideration indicates that our assessment of the RIC could be
improved by taking into account the replica symmetry breaking.
