  The goal of this work is to study the existence and properties of non
constant entire curves f drawn in a complex irreducible n-dimensional variety
X, and more specifically to show that they must satisfy certain global
algebraic or differential equations as soon as X is projective of general type.
By means of holomorphic Morse inequalities and a probabilistic analysis of the
cohomology of jet spaces, we are able to reach a significant step towards a
generalized version of the Green-Griffiths-Lang conjecture.
