The Brownian plane with minimal neck baby universe. Issue 4 (12th April 2017) - Wen, Yuting
Abstract: For each n ∈ ℕ, let Q n be a uniform rooted quadrangulation, endowed with an appropriate measure, of size n conditioned to have r ( n ) vertices in its root block. We prove that for a suitable function r ( n ), after rescaling graph distance by ( 21 40 · r ( n ) ) 1 / 4, Q n converges to a random pointed non‐compact metric measure space S, in the local Gromov‐Hausdorff‐Prokhorov topology. The space S is built by identifying a uniform point of the Brownian map with the distinguished point of the Brownian plane. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 729–752, 2017