scholarly journals Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach

2018 ◽  
Vol 2018 (6) ◽  
Author(s):  
Maciej A. Nowak ◽  
Wojciech Tarnowski
Keyword(s):  
Matrix Models ◽  
Hermitian Matrix

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

scholarly journals Factorisations for partition functions of random Hermitian matrix models

1996 ◽  
Vol 179 (1) ◽  
pp. 25-59 ◽  
Author(s):  
D. M. Jackson ◽  
M. J. Perry ◽  
T. I. Visentin
Keyword(s):  
Matrix Models ◽  
Hermitian Matrix ◽  
Partition Functions

NEW CRITICAL BEHAVIORS FOR ONE-HERMITIAN-MATRIX MODELS

1992 ◽  
Vol 07 (07) ◽  
pp. 1527-1551
Author(s):  
P.M.S. PETROPOULOS
Keyword(s):  
Matrix Models ◽  
Hermitian Matrix ◽  
Scaling Limit ◽  
Field Theories ◽  
Polynomial Coefficients ◽  
Multicritical Points ◽  
Exact Correlation Functions ◽  
Genus One ◽  
Exact Correlation ◽  
Double Scaling Limit

In the general framework of one-Hermitian-matrix models, we study critical behaviors such that δx~δRm/n~δSm; δx, δS and δR are, respectively, the bare cosmological constant and the orthogonal-polynomial coefficients around criticality. On the sphere, we prove the existence of consistent multicriticality conditions such that string equations exhibit the above behavior. We define a double scaling limit and write down exact equations for the specific heat for any (m, n) model. Their solutions are unambiguous and the only corrections come from genus-one topology. We compute exact correlation functions for well-defined scaling operators. These belong to two different sectors. One of them is such that any squared operator vanishes when inserted in any correlation function. We discuss briefly the flows between these multicritical points as well as the nature of the 2D field theories coupled to gravity which they can describe.

scholarly journals Bulk Universality and Related Properties of Hermitian Matrix Models

2007 ◽  
Vol 130 (2) ◽  
pp. 205-250 ◽  
Author(s):  
L. Pastur ◽  
M. Shcherbina
Keyword(s):  
Matrix Models ◽  
Hermitian Matrix

scholarly journals SUPERMATRIX MODELS

1992 ◽  
Vol 07 (24) ◽  
pp. 6105-6120 ◽  
Author(s):  
SCOTT A. YOST
Keyword(s):  
Matrix Models ◽  
Random Matrix ◽  
Stationary Point ◽  
Hermitian Matrix ◽  
Natural Extension ◽  
One Dimension ◽  
Two Component ◽  
Component Plasma ◽  
Random Matrix Models

Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous bosonic models. Two choices of integration slice are investigated. One leads to a perturbative structure which is reminiscent of, and perhaps identical to, the usual Hermitian matrix models. Another leads to an eigenvalue reduction which can be described by a two-component plasma in one dimension. A stationary point of the model is described.

scholarly journals THE WEINGARTEN MODEL À LA POLYAKOV

1992 ◽  
Vol 07 (18) ◽  
pp. 1651-1660 ◽  
Author(s):  
SIMON DALLEY
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Critical Behavior ◽  
Continuum Limit ◽  
Hermitian Matrix ◽  
Gauge Model ◽  
Vertex Models ◽  
Lattice Gauge ◽  
Genus Expansion ◽  
The Continuum

The Weingarten lattice gauge model of Nambu-Goto strings is generalized to allow for fluctuations of an intrinsic worldsheet metric through a dynamical quadrilation. The continuum limit is taken for c≤1 matter, reproducing the results of Hermitian matrix models to all orders in the genus expansion. For the compact c=1 case the vortices are Wilson lines, whose exclusion leads to the theory of non-interacting fermions. As a by-product of the analysis one finds the critical behavior of SOS and vertex models coupled to 2D quantum gravity.

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