  We build a model to predict from first principles the properties of major
mergers. We predict these from the coalescence of peaks and saddle points in
the vicinity of a given larger peak, as one increases the smoothing scale in
the initial linear density field as a proxy for cosmic time. To refine our
results, we also ensure, using a suite of $\sim 400$ power-law Gaussian random
fields smoothed at $\sim 30$ different scales, that the relevant peaks and
saddles are topologically connected: they should belong to a persistent pair
before coalescence. Our model allows us to (a) compute the probability
distribution function of the satellite-merger separation in Lagrangian space:
they peak at three times the smoothing scale; (b) predict the distribution of
the number of mergers as a function of peak rarity: halos typically undergo two
major mergers ($>$1:10) per decade of mass growth; (c) recover that the typical
spin brought by mergers: it is of the order of a few tens of per cent.

Cosmology and Nongalactic Astrophysics;Astrophysics of Galaxies