Gheorghe Bucur
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Starting with a Galton-Watson process $(Z_n)_n$ having $\mu_0=(\lambda_n)_n$ as initial distribution and $\mu=(\mu_n)_n$ the "reproduction law on $\mathbb{N}$" the problem of \emph{non-extinction} of $(Z_n)_n$ is strongly related to $\mu$. We give some relation of this phenomena with the compactness of the sequence $(Z_n)_n$ sometimes given by the law $\mu$ itself. The ingredient used in the proof is a converse of Tchebyshev's inequality.