CONVERGENCE DE CARTES NON - BIPARTIES VIA LA SYMÉTRISATION D’ARBRES ÉTIQUETÉS

— Fix an odd integer p ≥ 5. Let M_n be a uniform p-angulation with n vertices, endowed with the uniform probability measure on its vertices. We prove that there exists C_p ∈ R₊ such that, after rescaling distances by C_p/n^1/4, M_n converges in distribution for the Gromov–Hausdorff–Prokhorov topology towards the Brownian map. To prove the pre-ceding fact, we introduce a bootstrapping principle for distributional convergence of random labelled plane trees. In particular, the latter allows to obtain an invariance principle for labeled multitype Galton–Watson trees, with only a weak assumption on the centering of label displacements.