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 humankind, in conjunction with a deterministic generalized logistic model for humans-forest interaction and we evaluate the probability of avoiding the self-destruction of our civilization. Based on the current resource consumption rates and the best estimate of technological rate growth our study shows that we have a very low probability, less than 10% in the most optimistic estimate, to survive without facing a catastrophic collapse.
