  We study the long-time asymptotics of solutions of the uniformly parabolic
equation \[ u_t + F(D^2u) = 0 \quad {in} \R^n\times \R_+, \] for a positively
homogeneous operator $F$, subject to the initial condition $u(x,0) = g(x)$,
under the assumption that $g$ does not change sign and possesses sufficient
decay at infinity. We prove the existence of a unique positive solution
$\Phi^+$ and negative solution $\Phi^-$, which satisfy the self-similarity
relations \[ \Phi^\pm (x,t) = \lambda^{\alpha^\pm} \Phi^\pm (\lambda^{1/2} x,
\lambda t). \] We prove that the rescaled limit of the solution of the Cauchy
problem with nonnegative (nonpositive) initial data converges to $\Phi^+$
($\Phi^-$) locally uniformly in $\R^n \times \R_+$. The anomalous exponents
$\alpha^+$ and $\alpha^-$ are identified as the principal half-eigenvalues of a
certain elliptic operator associated to $F$ in $\R^n$.
