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Convergence of random polygon sequences

Incheoul Chung, Xingping Sun and Songfeng Zheng

Vol. 15 (2022), No. 4, 547–558
Abstract

We study stochastic convergence of random polygon sequences and establish several criteria for a sequence of random polygons to converge almost surely to a random limit point. We also explore a special case in which the limit point is prescribed. Existing literature on convergence of polygon sequences can be considered as a case study herein when all the participating random variables obey Dirac delta distributions.

Keywords
ergodicity coefficients, Markov chains, random matrices, random polygons, stochastic convergence.
Mathematical Subject Classification 2010
Primary: 15B52, 60G20
Secondary: 15A12, 15A30
Milestones
Received: 15 January 2019
Revised: 4 January 2022
Accepted: 12 January 2022
Published: 7 January 2023

Communicated by Zuhair Nashed
Authors
Incheoul Chung
Department of Mathematics
Cornell University
Ithaca, NY
United States
Xingping Sun
Department of Mathematics
Missouri State University
Springfield, MO
United States
Songfeng Zheng
Department of Mathematics
Missouri State University
Springfield, MO
United States