1,136 research outputs found

    The asymmetric ABAB matrix model

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    In this letter, it is pointed out that the two matrix model defined by the action S=(1/2)(tr A^2+tr B^2)-(alpha_A/4) tr A^4-(alpha_B/4) tr B^4-(beta/2) tr(AB)^2 can be solved in the large N limit using a generalization of the solution of Kazakov and Zinn-Justin (who considered the symmetric case alpha_A=alpha_B). This model could have useful applications to 3D Lorentzian gravity.Comment: 7 pages, 1 figur

    Proof of Razumov-Stroganov conjecture for some infinite families of link patterns

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    We prove the Razumov--Stroganov conjecture relating ground state of the O(1) loop model and counting of Fully Packed Loops in the case of certain types of link patterns. The main focus is on link patterns with three series of nested arches, for which we use as key ingredient of the proof a generalization of the Mac Mahon formula for the number of plane partitions which includes three series of parameters

    Jucys-Murphy elements and Weingarten matrices

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    We provide a compact proof of the recent formula of Collins and Matsumoto for the Weingarten matrix of the orthogonal group using Jucys-Murphy elements.Comment: v2: added a referenc

    Universality of correlation functions of hermitian random matrices in an external field

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    The behavior of correlation functions is studied in a class of matrix models characterized by a measure exp(S)\exp(-S) containing a potential term and an external source term: S=N\tr(V(M)-MA). In the large NN limit, the short-distance behavior is found to be identical to the one obtained in previously studied matrix models, thus extending the universality of the level-spacing distribution. The calculation of correlation functions involves (finite NN) determinant formulae, reducing the problem to the large NN asymptotic analysis of a single kernel KK. This is performed by an appropriate matrix integral formulation of KK. Multi-matrix generalizations of these results are discussed.Comment: 29 pages, Te

    The General O(n) Quartic Matrix Model and its application to Counting Tangles and Links

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    The counting of alternating tangles in terms of their crossing number, number of external legs and connected components is presented here in a unified framework using quantum field-theoretic methods applied to a matrix model of colored links. The overcounting related to topological equivalence of diagrams is removed by means of a renormalization scheme of the matrix model; the corresponding ``renormalization equations'' are derived. Some particular cases are studied in detail and solved exactly.Comment: 21 page
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