  A statistical mechanism is proposed for symmetrization of an extra space. The
conditions and rate of attainment of a symmetric configuration and, as a
consequence, the appearance of gauge invariance in low-energy physics is
discussed. It is shown that, under some conditions, this situation occurs only
after completion of the inflationary stage. The dependence of the constants
$\hbar$ and G on the geometry of the extra space and the initial parameters of
the Lagrangian of the gravitational field with higher derivatives are analyzed.
