No abstract

Using the Gell-Mann-Oakes-Renner (GOR) relation and semi-classical arguments, we show that the bulk quark spectrum in QCD exhibits a variety of regimes including the ergodic one described by random matrix theory. We analyze the quark spectral form-factor in the diffusive and ballistic regime. We suggest that a class of chiral transitions in QCD is possibly of the metal-insulator type, with a universal spectral statistics at the mobility edge

Using the standard concepts of free random variables, we show that for a large class of nonhermitean random matrix models, the support of the eigenvalue distribution follows from their hermitean analogs using a conformal transformation. We also extend the concepts of free random variables to the class of nonhermitean matrices, and apply them to the models discussed by Ginibre-Girko (elliptic ensemble) and Mahaux-Weidenmüller (chaotic resonance scattering).

We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for non-hermitian random-matrix models in the large-N limit. We apply this result to a number of non-hermitian random-matrix models and show that the outcome is in good agreement with numerical results.

We apply the concept of free random variables to doubly correlated (Gaussian) Wishart random matrix models, appearing, for example, in a multivariate analysis of financial time series, and displaying both inter-asset cross-covariances and temporal auto-covariances. We give a comprehensive introduction to the rich financial reality behind such models. We explain in an elementary way the main techniques of free random variables calculus, with a view to promoting them in the quantitative finance community. We apply our findings to tackle several financially relevant problems, such as a universe of assets displaying exponentially decaying temporal covariances, or the exponentially weighted moving average, both with an arbitrary structure of cross-covariances.Portfolio theory, Power laws, Statistical physics, Risk measures, Random walks, Options pricing, Random matrix theory,

No abstract

We use a chiral random matrix model with 2N f flavors to mock up the QCD Dirac spectrum at finite chemical potential. We show that the 1/N approximation breaks down in the quenched state with spontaneously broken chiral symmetry. The breakdown condition is set by the divergence of a two-point function, that is shown to follow the general lore of macroscopic universality. In this state, the fermionic fluctuations are not suppressed in the large N limit.1. In the presence of a chemical potential, the lattice QCD Dirac operator is non-hermitean. As a result, the fermionic determinant (probability measure) of the QCD Dirac operator is a complex number. Since Monte-Carlo simulations demand a positive definite measure, straightforward algorithms have failed [1]. Unconventional QCD algorithms have been devised, leading to a chiral phase transition at finite chemical potential and strong coupling (g = ∞) [1][2][3]. In the quenched approximation, however, the restoration of chiral symmetry was found to set in at surprisingly small chemical potentials of the order of half the pion mass, thereby vanishing in the chiral limit [4]. The origin of the discrepancy was traced back to the phase of the Dirac operator [5], as demonstrated by in [3] using lattice simulations.While many of the basic issues related to the quenched calculations are known on the lattice [2-5], we feel the need for a better understanding using simple models. The spontaneous breaking of chiral symmetry in QCD reflects the spectral distribution of quark eigenvalues near zero-virtuality [6]. For sufficiently random gauge configurations, the Dirac operator can be approximated by a chiral matrix with random entries [7,8], in qualitative agreement with a number of lattice simulations for both the bulk eigenvalue distributions [9], and correlations [10,11].Chiral random matrix models with finite chemical potential have been discussed recently in [12-14] using various methods. For zero chemical potential, the ground state breaks spontaneously chiral symmetry. The lowlying spectrum is that of constituent quarks with no Fermi surface. Naively one would expect that for a chemical potential of the order of the constituent quark mass, chiral symmetry would be restored. This expectation is not borne out by direct numerical calculations which show that chiral symmetry is restored for any nonzero chemical potential in the chiral limit and for large matrix sizes [12], in qualitative agreement with the quenched lattice simulations. The numerical results have been shown to follow from a modified replica trick [12,15], in agreement with [3].In this letter, we reanalyze the spectral density with 2N f conventional quarks. In section 2, we introduce the model and discuss the 1/N expansion around the quenched state with spontaneously broken chiral symmetry. In section 3, we evaluate a pertinent two-point correlation in the same state, and show that it diverges in the eigenvalue plane in the small eigenvalue region. The support for the ensuing spectral distribution is in agreeme...

Predictions made in Albacete et al. [Int. J. Mod. Phys. E 22 (2013) 1330007] prior to the LHC [Formula: see text]Pb run at [Formula: see text] TeV are compared to currently available data. Some predictions shown here have been updated by including the same experimental cuts as the data. Some additional predictions are also presented, especially for quarkonia, that were provided to the experiments before the data were made public but were too late for the original publication.