Geodesic
Topological recursion for Gaussian means and cohomological field
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 371-409

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We introduce explicit relations between genus-filtrated $s$-loop means of the Gaussian matrix model and terms of the genus expansion of the Kontsevich–Penner matrix model (KPMM{), which is the generating function for volumes of discretized (openm) moduli spaces $M_{g,s}^\mathrm{disc}$ (discrete volumes). Using these relations, we express Gaussian means in all orders of the genus expansion as polynomials in special times weighted by ancestor invariants of an underlying cohomological field theory. We translate the topological recursion of the Gaussian model into recurrence relations for the coefficients of this expansion, which allows proving that they are integers and positive. We find the coefficients in the first subleading order for $\\mathcal M_{g,1}$ for all $g$ in three ways: using the refined Harer–Zagier recursion, using the Givental-type decomposition of the KPMM, and counting diagrams explicitly.
Keywords: chord diagram, Kontsevich–Penner matrix model, discrete volume, Deligne–Mumford compactification.
Mots-clés : Givental decomposition, moduli space 
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     author = {J. E. Andersen and L. O. Chekhov and P. Norbury and R. C. Penner},
     title = {Topological recursion for {Gaussian} means and cohomological field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {371--409},
     publisher = {mathdoc},
     volume = {185},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a0/}
}
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J. E. Andersen; L. O. Chekhov; P. Norbury; R. C. Penner. Topological recursion for Gaussian means and cohomological field. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 371-409. http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a0/