High dimensional analogue of metric distortion for simplicial complexes

2014/12/22 by Izhar Oppenheim, Oppenheim, Izhar
Computer Science · Mathematics · #05C80 #05E45 #52C99 #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Metric Geometry (math.MG) #Point processes and geometric inequalities #Topological and Geometric Data Analysis #math.CO #math.MG #msc:05C80 #msc:05E45 #msc:52C99

paper · pdf · doi:10.48550/arxiv.1412.7142

21 pages

arxiv created 2014/12/22 · openalex publication_date 2014/12/22 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We suggest a new possible high dimensional analogue to metric distortion. We then show a possible method for providing lower bounds to this distortion and use this method to prove a "Bourgain-type" distortion theorem for Linial-Meshulam random complexes.

Related

• Higher dimensional distortion of random complexes
• On the Dimension of Random Simplicial Complexes
• Topology of random geometric complexes: a survey
• Generalized Random Simplicial Complexes
• Large Random Simplicial Complexes, III; The Critical Dimension