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Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces

Andersen, Jørgen E. and Chekhov, Leonid O. and Penner, R. C. and Reidys, Christian M. and Sułkowski, Piotr (2013) Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces. Nuclear Physics B, 866 (3). pp. 414-443. ISSN 0550-3213.

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We introduce and study the Hermitian matrix model with potential V_(s,t)(x)=x^2/2−stx/(1−tx), which enumerates the number of linear chord diagrams with no isolated vertices of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are convergent for small t and all s as a perturbation of the Gaussian potential, which arises for st=0. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given topology as well as the number of cells in Riemannʼs moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly in genus less than four.

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Additional Information:© 2012 Elsevier B. V. Received 23 May 2012; accepted 17 September 2012; Available online 20 September 2012. JEA and RCP are supported by the Centre for Quantum Geometry of Moduli Spaces which is funded by the Danish National Research Foundation. The research of LCh is supported by the Russian Foundation for Basic Research (Grants Nos. 10-02-01315-a, 11-01-12037-ofi-m-2011, and 11-02-90453-Ukr-f-a) by the Program Mathematical Methods of Nonlinear Dynamics and by the Grant of Supporting Leading Scientific Schools NSh-4612.2012.1. The research of PS is supported by the DOE grant DE-FG03-92-ER40701FG-02, the European Commission under the Marie-Curie International Outgoing Fellowship Programme, and the Foundation for Polish Science. RCP also acknowledges the kind support of Institut Henri Poincaré where parts of this manuscript were written.
Funding AgencyGrant Number
Danish National Research Foundation Centre for Quantum Geometry of Moduli SpacesUNSPECIFIED
Russian Foundation for Basic Research10-02-01315-a
Russian Foundation for Basic Research11-01-12037-ofi-m-2011
Russian Foundation for Basic Research11-02-90453-Ukr-f-a
Program Mathematical Methods of Nonlinear DynamicsUNSPECIFIED
Grant of Supporting Leading Scientific SchoolsNSh-4612.2012.1
Department of Energy (DOE)DE-FG03-92-ER40701FG-02
Marie-Curie International Outgoing Fellowship Programme European CommissionUNSPECIFIED
Foundation for Polish ScienceUNSPECIFIED
Institut Henri PoincaréUNSPECIFIED
Subject Keywords:Chord diagrams; Matrix model; Riemannʼs moduli space; RNA; Topological recursion
Issue or Number:3
Record Number:CaltechAUTHORS:20121126-134532713
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Official Citation:Jørgen E. Andersen, Leonid O. Chekhov, R.C. Penner, Christian M. Reidys, Piotr Sułkowski, Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces, Nuclear Physics B, Volume 866, Issue 3, 21 January 2013, Pages 414-443, ISSN 0550-3213, 10.1016/j.nuclphysb.2012.09.012.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:35643
Deposited By: Jason Perez
Deposited On:26 Nov 2012 22:05
Last Modified:03 Oct 2019 04:30

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