Chain of matrices, loop equations and topological recursion

Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is n...

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Autor principal: Orantin, Nicolas
Lenguaje:eng
Publicado: 2009
Materias:
Mathematical Physics and Mathematics
Acceso en línea:http://cds.cern.ch/record/1225621
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author Orantin, Nicolas
author_facet Orantin, Nicolas
author_sort Orantin, Nicolas
collection CERN
description Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.
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spelling cern-12256212021-07-16T18:14:52Zhttp://cds.cern.ch/record/1225621engOrantin, NicolasChain of matrices, loop equations and topological recursionMathematical Physics and MathematicsRandom matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. These two definitions, perturbative and non-perturbative, are discussed in this chapter as well as their relation. The so-called loop equations satisfied by integrals over random matrices coupled in chain is discussed as well as their recursive solution in the perturbative case when the matrices are Hermitean.arXiv:0911.5089CERN-PH-TH-2009-233CERN-PH-TH-2009-233oai:cds.cern.ch:12256212009-11-30
spellingShingle Mathematical Physics and Mathematics
Orantin, Nicolas
Chain of matrices, loop equations and topological recursion
title Chain of matrices, loop equations and topological recursion
title_full Chain of matrices, loop equations and topological recursion
title_fullStr Chain of matrices, loop equations and topological recursion
title_full_unstemmed Chain of matrices, loop equations and topological recursion
title_short Chain of matrices, loop equations and topological recursion
title_sort chain of matrices, loop equations and topological recursion
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/1225621
work_keys_str_mv AT orantinnicolas chainofmatricesloopequationsandtopologicalrecursion

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