  We apply Tsallis's q-indexed entropy to formulate a non-extensive random
matrix theory (RMT), which may be suitable for systems with mixed
regular-chaotic dynamics. The joint distribution of the matrix elements is
given by folding the corresponding quantity in the conventional random matrix
theory by a distribution of the inverse matrix-element variance. It keeps the
basis invariance of the standard theory but violates the independence of the
matrix elements. We consider the sub-extensive regime of q more than unity in
which the transition from the Wigner to the Poisson statistics is expected to
start. We calculate the level density for different values of the entropic
index. Our results are consistent with an analogous calculation by Tsallis and
collaborators. We calculate the spacing distribution for mixed systems with and
without time-reversal symmetry. Comparing the result of calculation to a
numerical experiment shows that the proposed non-extensive model provides a
satisfactory description for the initial stage of the transition from chaos
towards the Poisson statistics.
