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math.PR2021★ 2 cited
The mesoscopic geometry of sparse random maps
Nicolas Curien, Igor Kortchemski, Cyril Marzouk
We investigate the structure of large uniform random maps with edges, faces, and with genus in the so-called sparse case, where the ratio between…
math.PR2021★ 4 cited
Large deviation Local Limit Theorems and limits of biconditioned Trees and Maps
Igor Kortchemski, Cyril Marzouk
We first establish new local limit estimates for the probability that a nondecreasing integer-valued random walk lies at time at an arbitrary value, encompassing in particular…