  We present an application of Large Deviation Theory to the problem of
structure growth on large-scale structure cosmology. Starting from gaussian
distributed overdensities on concentric spherical shells, we show that a Large
Deviation Principle holds for the densities on the corresponding shells after
gravitational evolution if no shell-crossing happens. As consequences of the
Large Deviation Principle we obtain the cumulant generating function for the
non-linear densities, and present formulae to compute the cumulant generating
function for general window functions.
