Rate of degeneracy of two point densities. Application to lowerbounds of hitting probabilities

We consider nonlinear stochastic wave equations in dimension d\le 3.

Using Malliavin Calculus, we give upper bounds for the small eigenvalues of the inverse of two point densities.These provide a rate of degeneracy when points go close to each other.  Then, we analyze the consequences of this result on lower estimates for hitting probabilities.