ON THE SCALING LIMIT OF RANDOM PLANAR MAPS WITH LARGE FACES

We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index alpha is an element of (1, 2). We view the vertex-set of a map as a metric space by endowing it with the usual graph distance. When the number n of vertices of the map tends to infinity, this metric space, rescaled by the factor n(-> 1/2 alpha), converges in distribution as n -> infinity, at least along suitable subsequences, towards a limiting random compact metric space whose Hausdorff dimension is equal to 2 alpha. This is a short presentation of the article [1], to which the interested reader is referred for more details.