  In this paper we afford a quantitative analysis of the sustainability of
current world population growth in relation to the parallel deforestation
process adopting a statistical point of view. We consider a simplified model
based on a stochastic growth process driven by a continuous time random walk,
which depicts the technological evolution of human kind, in conjunction with a
deterministic generalised logistic model for humans-forest interaction and we
evaluate the probability of avoiding the self-destruction of our civilisation.
Based on the current resource consumption rates and best estimate of
technological rate growth our study shows that we have very low probability,
less than 10% in most optimistic estimate, to survive without facing a
catastrophic collapse.
