Random words in free groups, non-crossing matchings and RNA secondary structures

2020/07/23 by Siddhartha Gadgil, Gadgil, Siddhartha, Manjunath Krishnapur +1
Biochemistry, Genetics and Molecular Biology · #20F12 #20F65 #FOS: Mathematics #Genomics and Chromatin Dynamics #Geometric Topology (math.GT) #Group Theory (math.GR) #Probability (math.PR) #RNA Research and Splicing #RNA and protein synthesis mechanisms

paper · pdf · doi:10.48550/arxiv.2007.12109

openalex publication_date 2020/07/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Consider a random word Xⁿ=(X₁,… ,X_n) in an alphabet consisting of 4 letters, with the letters viewed either as A, U, G and C (i.e., nucleotides in an RNA sequence) or α, α, β and β (i.e., generators of the free group ⟨α,β⟩ and their inverses). We show that the expected fraction ρ(n) of unpaired bases in an optimal RNA secondary structure (with only Watson-Crick bonds and no pseudo-knots) converges to a constant λ₂ with 0

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