LNRE stands for "large number of arre events", a term, which I introduced in my still unpublished report, CWI, Amsterdam, in 1989. The theory of LNRE can also be called the "Statistical Theory of Diversity". All this is a subject of old, although slowly evolving, interests of mine. Too many things here to describe in few lines. But the topic ahs enourmous potencial for discovery and advance in understanding. We basically see things and discribe them, but we do not understand them.
One recent paper in this direction is here
. The title of this paper is very uninformative: it should have been "On occupancy problems in high-dimensional spaces".