The Brownian plane with minimal neck baby universe. Issue 4 (12th April 2017)

• Record Type: Journal Article
• Authors: Wen, Yuting
• Is Part Of: Random structures & algorithms. Volume 51:Issue 4(2017)
• Page Start: 729
• Page End: 752
• Publication Date: 2017-04-12
• Subjects: Brownian map -- Brownian plane -- scaling limit -- local Gromov‐Hausdorff‐Prokhorov topology -- quadrangulation -- connectivity -- core -- condensation -- random allocation; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20722
• Languages: English
• ISSNs: 1042-9832

Abstract

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