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

Estimating major merger rates and spin parameters ab initio via the clustering of critical events