Limit Distributions of Products of Independent and Identically Distributed Random 2 × 2 Stochastic Matrices: A Treatment with the Reciprocal of the Golden Ratio

Authors

Santanu Chakraborty, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

12-18-2023

Abstract

Consider a sequence (Xn)n≥1 of i.i.d. 2×2 stochastic matrices with each Xn distributed as μ. This μ is described as follows. Let (Cn,Dn)T denote the first column of Xn and for a given real r with 012 is very challenging. Considering the extreme nontriviality of this case, we stick to a very special such r, namely, r=√5−12 (the reciprocal of the golden ratio), briefly mention the challenges in this nontrivial case, and completely identify λ for a very special situation.

Comments

© 2023 by the author. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Recommended Citation

Chakraborty, Santanu. "Limit Distributions of Products of Independent and Identically Distributed Random 2× 2 Stochastic Matrices: A Treatment with the Reciprocal of the Golden Ratio." Mathematics 11, no. 24 (2023): 4993. https://doi.org/10.3390/math11244993

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Mathematics

DOI

10.3390/math11244993