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Monge-Amp\`ere gravitation is a modification of the classical Newtoniangravitation where the linear Poisson equation is replaced by the nonlinearMonge-Amp\`ere equation. This paper is concerned with the rigorous derivationof Monge-Amp\`ere gravitation for a finite number of particles from thestochastic model of a Brownian point cloud, in the spirit of a previous work bythe third author [A double large deviation principle for Monge-Amp\`eregravitation, 2016]. The main step in this derivation is the$\Gamma-$convergence of the good rate functions corresponding to aone-parameter family of large deviation principles. Surprisingly, the derivedmodel includes dissipative phenomena. As an illustration, we show that it leadsto sticky collisions in one space dimension.

Monge-Amp\`ere gravitation as a $\Gamma$-limit of good rate functions