# Loop equation analysis of the circular β ensembles

@article{Witte2015LoopEA, title={Loop equation analysis of the circular β ensembles}, author={Nicholas S. Witte and Peter J. Forrester}, journal={Journal of High Energy Physics}, year={2015}, volume={2015}, pages={1-42} }

A bstractWe construct a hierarchy of loop equations for invariant circular ensembles. These are valid for general classes of potentials and for arbitrary inverse temperatures Re β > 0 and number of eigenvalues N. Using matching arguments for the resolvent functions of linear statistics f(ζ) = (ζ + z)/(ζ − z) in a particular asymptotic regime, the global regime, we systematically develop the corresponding large N expansion and apply this solution scheme to the Dyson circular ensemble. Currently… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### Citations

##### Publications citing this paper.

SHOWING 1-6 OF 6 CITATIONS

## An Arithmetic Property of Moments of the β-Hermite Ensemble and Certain Map Enumerators

VIEW 1 EXCERPT

CITES METHODS

## Christian Linear statistics of the circular β-ensemble , stein ’ s method , and circular Dyson Brownian motion

VIEW 1 EXCERPT

CITES BACKGROUND

## circular Dyson Brownian motion

VIEW 1 EXCERPT

CITES BACKGROUND

## Linear statistics of the circular $\beta$-ensemble, Stein's method, and circular Dyson Brownian motion

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 40 REFERENCES

## Matrix eigenvalue model: Feynman graph technique for all genera

VIEW 7 EXCERPTS

HIGHLY INFLUENTIAL

## Random Matrices, volume 142 of Pure and Applied Mathematics (Amsterdam)

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## Statistical theory of the energy levels of complex systems. I

VIEW 22 EXCERPTS

HIGHLY INFLUENTIAL

## Log-Gases and Random Matrices

VIEW 4 EXCERPTS

## Unitary matrix models and phase transition

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Unitary matrix models with a topological term and discrete time Toda equation

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## UNITARY MATRIX MODELS AND PAINLEVÉ III

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## The uses of the refined matrix model recursion

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL