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We study plane trees as a model for RNA secondary structure, assigning energyto each tree based on the Nearest Neighbor Thermodynamic Model, and defining acorresponding Gibbs distribution on the trees. Through a bijection betweenplane trees and 2-Motzkin paths, we design a Markov chain converging to theGibbs distribution, and establish fast mixing time results by estimating thespectral gap of the chain. The spectral gap estimate is established through aseries of decompositions of the chain and also by building on known mixing timeresults for other chains on Dyck paths. In addition to the mathematical aspectsof the result, the resulting algorithm can be used as a tool for exploring thebranching structure of RNA and its dependence on energy model parameters. Thepseudocode implementing the Markov chain is provided in an appendix.

Markov Chain-based Sampling for Exploring RNA Secondary Structure under the Nearest Neighbor Thermodynamic Model