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2013

Enumeration of RNA complexes via random matrix theory

Andersen, Jørgen E., Chekhov, Leonid O., Penner, R. C. et al.

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We review a derivation of the numbers of RNA complexes of an arbitrary topology.

These numbers are encoded in the free energy of the hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), where s and t are respective generating parameters for the number of RNA molecules and hydrogen bonds in a given complex.
The free energies of this matrix model are computed using the so-called topological recursion, which is a powerful new formalism arising from random matrix theory.
These numbers of RNA complexes also have profound meaning in mathematics: they provide the number of chord diagrams of fixed genus with specified numbers of backbones and chords as well as the number of cells in Riemann's moduli spaces for bordered surfaces of fixed topological type.

Enumeration of RNA complexes via random matrix theory · Around

Built on

R. C. Penner, Perturbative series and the moduli space of Riemann surfaces,
1988
Earlier work this paper cites.
H. Orland and A. Zee, RNA folding and large N matrix theory
2002
Earlier work this paper cites.
L. Chekhov, B. Eynard, Hermitean matrix model free energy: Feynman graph technique for all genera , JHEP 0603 (2006) 014
2006
Earlier work this paper cites.

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Then

R. Penner, Decorated Teichmüller Theory , QGM Master Class Series, Volume 1, European Mathematical Society, Zürich (2012)
2012
Later among the works it cites.
J. Andersen, L. Chekhov, R. Penner, C. Reidys, P. Sułkowski, Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces , Nucl. Phys. B866 (2013) 414, [1205.0658 [hep-th]]
2013
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