### Abstract

We introduce an extension of the diagrammatic rules in random matrix theory and apply it to non-hermitian random matrix models using the 1/N approximation. A number of one-and two-point functions are evaluated on their holomorphic and non-holomorphic supports to leading order in 1/N. The one-point functions describe the distribution of eigenvalues, while the two-point functions characterize their macroscopic correlations. The generic form for the two-point functions is obtained, generalizing the concept of macroscopic universality to non-hermitian random matrices. We show that the holomorphic and non-holomorphic one-and two-point functions condition the behavior of pertinent partition functions to order script O sign(1/N). We derive explicit conditions for the location and distribution of their singularities. Most of our analytical results are found to be in good agreement with numerical calculations using large ensembles of complex matrices.

Original language | English |
---|---|

Pages (from-to) | 603-642 |

Number of pages | 40 |

Journal | Nuclear Physics B |

Volume | 501 |

Issue number | 3 |

Publication status | Published - Sep 22 1997 |

### Fingerprint

### Keywords

- Diagrammatic expansion
- Non-hermitian random matrix models
- Universal correlator

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*501*(3), 603-642.

**Non-hermitian random matrix models.** / Janik, Romuald A.; Nowak, Maciej A.; Papp, G.; Zahed, Ismail.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 501, no. 3, pp. 603-642.

}

TY - JOUR

T1 - Non-hermitian random matrix models

AU - Janik, Romuald A.

AU - Nowak, Maciej A.

AU - Papp, G.

AU - Zahed, Ismail

PY - 1997/9/22

Y1 - 1997/9/22

N2 - We introduce an extension of the diagrammatic rules in random matrix theory and apply it to non-hermitian random matrix models using the 1/N approximation. A number of one-and two-point functions are evaluated on their holomorphic and non-holomorphic supports to leading order in 1/N. The one-point functions describe the distribution of eigenvalues, while the two-point functions characterize their macroscopic correlations. The generic form for the two-point functions is obtained, generalizing the concept of macroscopic universality to non-hermitian random matrices. We show that the holomorphic and non-holomorphic one-and two-point functions condition the behavior of pertinent partition functions to order script O sign(1/N). We derive explicit conditions for the location and distribution of their singularities. Most of our analytical results are found to be in good agreement with numerical calculations using large ensembles of complex matrices.

AB - We introduce an extension of the diagrammatic rules in random matrix theory and apply it to non-hermitian random matrix models using the 1/N approximation. A number of one-and two-point functions are evaluated on their holomorphic and non-holomorphic supports to leading order in 1/N. The one-point functions describe the distribution of eigenvalues, while the two-point functions characterize their macroscopic correlations. The generic form for the two-point functions is obtained, generalizing the concept of macroscopic universality to non-hermitian random matrices. We show that the holomorphic and non-holomorphic one-and two-point functions condition the behavior of pertinent partition functions to order script O sign(1/N). We derive explicit conditions for the location and distribution of their singularities. Most of our analytical results are found to be in good agreement with numerical calculations using large ensembles of complex matrices.

KW - Diagrammatic expansion

KW - Non-hermitian random matrix models

KW - Universal correlator

UR - http://www.scopus.com/inward/record.url?scp=0031583540&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031583540&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031583540

VL - 501

SP - 603

EP - 642

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -