arXiv subjects

I. Zahed

Publications and source records attributed to I. Zahed.

At least 19 recordsLinked to original sources

arXiv2010

Applying Free Random Variables to Random Matrix Analysis of Financial Data. Part I: A Gaussian Case

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 the free random variables calculus, with a view to promote them in the quantitative finance community. We apply our findings to tackle several financially relevant problems, such as of an universe of assets displaying exponentially decaying temporal covariances, or the exponentially weighted moving average, both with an arbitrary structure of cross-covariances.

physics.soc-ph↗

arXiv2009

Low mass dilepton radiation at RHIC

In this work we discuss the emission of low mass dilepton radiation from a hydrodynamic evolution model of Au-Au collisions and make comparisons with recent PHENIX measurements. The dilepton emission rates from the hadronic phase are treated at finite temperature and baryon density and are completely constrained by broken chiral symmetry in a density expansion. The rates are expressed in terms of vacuum correlators which are measured in $e^+e^-$ annihilation, $τ$ decays and photo-reactions on nucleons and nuclei. We consider two possibilities for the hadronic phase: A chemical equilibrated an off equilibrium hadronic gas. We find that while chemical off-equilibrium helps explain part of the low mass (0.15 $\leq$ M GeV $\leq$ 0.7) enhancement seen in the data there is still a large discrepancy.

nucl-th↗

arXiv2008

A PNJL model in 0+1 Dimensions

We formulate the Polyakov-Nambu-Jona-Lasinio (PNJL) model in 0+1 dimensions. The thermodynamics captured by the partition function yields a bulk pressure, as well as quark susceptibilities versus temperature that are similar to the ones in 3+1 dimensions. Around the transition temperature the behavior in the pressure and quark susceptibilities follows from the interplay between the lowest Matsubara frequency and the Polyakov line. The reduction to the lowest Matsubara frequency yields a matrix Model. In the presence of the Polyakov line the UV part of the Dirac spectrum features oscillations when close to the transition temperature.

hep-ph↗

arXiv2006

Thermal Dimuon Yields at NA60

Dilepton emission rates from a hadronic gas at finite temperature and baryon density are completely constrained by broken chiral symmetry in a density expansion. The rates can be expressed in terms of vacuum correlations which are measured in $e^+e^-$ annihilation, $τ$ decays and photo-reactions on nucleons and nuclei. In this paper, the theoretical results are summarized and the total dimuon yield is calculated by integrating the dimuon rates over the space-time history of a fireball based on hydrodynamic calculations with CERN SPS conditions. The resulting dimuon yield is in good agreement with the recent measurements reported by NA60.

nucl-th↗

arXiv2002

Scattering Through QCD Sphalerons

Diffractive parton-parton scattering in the soft pomeron regime can be explained by the production of a QCD sphaleron. Sphaleron production results into the emission of $3+2N_F$ gluons and quarks. At RHIC we expect many sphalerons to be released thereby affecting most prompt processes.

hep-ph↗

arXiv2002

Jet Quenching in High Energy Heavy Ion Collisions by QCD Synchrotron-like Radiation

We consider synchrotron-like radiation in QCD by generalizing Schwinger's treatment of quantum synchrotron radiation in QED to the case of a constant chromomagnetic field. We suggest a novel mechanism for {\em jet quenching} in heavy ion collisions, whereby high-$p_t$ partons get depleted through strong (classical) color fields. The latters are encountered in the color glass condensate or in the form of expanding shells of exploding sphalerons. Unlike bremsstrahlung radiation through multiple soft rescattering, synchrotron radiation converts a jet into a wide shower of soft gluons. We estimate the energy loss through this mechanism and suggest that it contributes significantly to the unexpectedly strong jet quenching observed at RHIC.

hep-ph↗

arXiv2001

Isospin Fluctuations in QCD and Relativistic Heavy-Ion Collisions

We address the role of fluctuations in strongly interacting matter during the dense stages of a heavy-ion collision through its electromagnetic emission. Fluctuations of isospin charge are considered in a thermal system at rest as well as in a moving hadronic fluid at fixed proper time within a finite bin of pseudo-rapidity. In the former case, we use general thermodynamic relations to establish a connection between fluctuations and the space-like screening limit of the retarded photon self-energy, which directly relates to the emissivities of dileptons and photons. Effects of hadronic interactions are highlighted through two illustrative calculations. In the latter case, we show that a finite time scale $τ$ inherent in the evolution of a heavy-ion collision implies that equilibrium fluctuations involve both space-like and time-like components of the photon self-energy in the system. Our study of non-thermal effects, explored here through a stochastic treatment, shows that an early and large fluctuation in isospin survives only if it is accompanied by a large temperature fluctuation at freeze-out, an unlikely scenario in hadronic phases with large heat capacity. We point out prospects for the future which include: (1) A determination of the Debye mass of the system at the dilute freeze-out stage of a heavy-ion collision, and (2) A delineation of the role of charge fluctuations during the dense stages of the collision through a study of electromagnetic emissivities.

hep-ph↗

arXiv2001

Free Random Levy Variables and Financial Probabilities

We suggest that Free Random Variables, represented here by large random matrices with spectral Levy disorder, may be relevant for several problems related to the modeling of financial systems. In particular, we consider a financial covariance matrix composed of asymmetric and free random Levy matrices. We derive an algebraic equation for the resolvent and solve it to extract the spectral density. The free eigenvalue spectrum is in remarkable agreement with the one obtained from the covariance matrix of the SP500 financial market.

cond-mat↗

arXiv2001

Levy Matrices and Financial Covariances

In a given market, financial covariances capture the intra-stock correlations and can be used to address statistically the bulk nature of the market as a complex system. We provide a statistical analysis of three SP500 covariances with evidence for raw tail distributions. We study the stability of these tails against reshuffling for the SP500 data and show that the covariance with the strongest tails is robust, with a spectral density in remarkable agreement with random Levy matrix theory. We study the inverse participation ratio for the three covariances. The strong localization observed at both ends of the spectral density is analogous to the localization exhibited in the random Levy matrix ensemble. We discuss two competitive mechanisms responsible for the occurrence of an extensive and delocalized eigenvalue at the edge of the spectrum: (a) the Levy character of the entries of the correlation matrix and (b) a sort of off-diagonal order induced by underlying inter-stock correlations. (b) can be destroyed by reshuffling, while (a) cannot. We show that the stocks with the largest scattering are the least susceptible to correlations, and likely candidates for the localized states. We introduce a simple model for price fluctuations which captures behavior of the SP500 covariances. It may be of importance for assets diversification.

cond-mat↗

arXiv2001

Free Levy Matrices and Financial Correlations

We consider a covariance matrix composed of asymmetric and free random Levy matrices. We use the results of free random variables to derive an algebraic equation for the resolvent and solve it to extract the spectral density. For an appropriate choice of asymmetry and Levy index ($α/2=3/4$) the free eigenvalue spectrum is in remarkable agreement with the one obtained from the covariance matrix of the SP500 financial market. Our results are of interest to a number of stochastic systems with power law noise.

cond-mat↗

arXiv2001

Wealth Condensation in Pareto Macro-Economies

We discuss a Pareto macro-economy (a) in a closed system with fixed total wealth and (b) in an open system with average mean wealth and compare our results to a similar analysis in a super-open system (c) with unbounded wealth. Wealth condensation takes place in the social phase for closed and open economies, while it occurs in the liberal phase for super-open economies. In the first two cases, the condensation is related to a mechanism known from the balls-in-boxes model, while in the last case to the non-integrable tails of the Pareto distribution. For a closed macro-economy in the social phase, we point to the emergence of a ``corruption'' phenomenon: a sizeable fraction of the total wealth is always amassed by a single individual.

cond-mat.stat-mech↗

arXiv2000

Free Random Levy Matrices

Using the theory of free random variables (FRV) and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable Lévy distributions. We show that the resolvents for the corresponding matrices obey transcendental equations in the large size limit. We solve these equations in a number of cases, and show that the eigenvalue distributions exhibit Lévy tails. For the analytically known Lévy measures we explicitly construct the density of states using the method of orthogonal polynomials. We show that the Lévy tail-distributions are characterized by a novel form of microscopic universality.

cond-mat.mes-hall↗

arXiv2000

A chiral crystal in cold QCD matter at intermediate densities?

The analogue of Overhauser (particle-hole) pairing in electronic systems (spin-density waves with non-zero total momentum $Q$) is analyzed in finite-density QCD for 3 colors and 2 flavors, and compared to the color-superconducting BCS ground state (particle-particle pairing, $Q$=0). The calculations are based on effective nonperturbative four-fermion interactions acting in both the scalar diquark as well as the scalar-isoscalar quark-hole ('$σ$') channel. Within the Nambu-Gorkov formalism we set up the coupled channel problem including multiple chiral density wave formation, and evaluate the resulting gaps and free energies. Employing medium-modified instanton-induced 't Hooft interactions, as applicable around $μ_q\simeq 0.4$ GeV (or 4 times nuclear saturation density), we find the 'chiral crystal phase' to be competitive with the color superconductor.

hep-ph↗

arXiv1999

Correlations of Eigenvectors for Non-Hermitian Random-Matrix Models

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.

cond-mat↗

arXiv1998

Thermal Dileptons from a Nonperturbative Quark-Gluon Phase

Assuming that gluon condensates are important even above the deconfining phase transition, we develop a model for the dilepton yield from a quark gluon plasma. Using a simple fire ball description of a heavy ion collision, and various estimates of the strengths of the gluon condensates, we compare our predicted dilepton yields with those observed in the CERES and HELIOS experiments at CERN. The simple model gives an adequate description of the data, and in particular it explains the observed considerable enhancement of the yield in the low mass region.

hep-ph↗

arXiv1998

Master Formulae Approach to Photon Fusion Reactions

We analyze the $γγ\to ππ, KK, ηη, πη$ reactions through $\sqrt{s}=2$ GeV, using the master formula approach to QCD with three flavors. In this approach, the constraints of broken chiral symmetry, unitarity and crossing symmetry are manifest in all channels. The pertinent vacuum correlators are analyzed at tree level using straightforward resonance saturation methods. A one-loop chiral power counting analysis at treshold is also carried out and compared to standard chiral perturbation theory. Our results are in overall agreement with the existing data in all channels. We predict the strange meson polarizabilities and a very small cross section for $γγ\toηη$.

hep-ph↗

arXiv1998

Dilepton and Photon Emission Rates from a Hadronic Gas III

We extend our early analyses of the dilepton and photon emission rates from a hadronic gas to account for strange mesons using a density expansion. The emission rates are reduced to vacuum correlation functions using three-flavor chiral reduction formulas, and the latters are assessed in terms of empirical data. Using a fire-ball, we compare our results to the low and intermediate mass dilepton data available from CERN. Our results suggest that a baryon free hadronic gas does not account for the excess of low mass dielectrons observed at CERES but do well in accounting for the intermediate dimuons at HELIOS. The same observations apply to the recent low and high $p_t$ dielectron rates from CERES.

hep-ph↗

arXiv1998

Critical Scaling at Zero Virtuality in QCD

We show that at the critical point of chiral random matrix models, novel scaling laws for the inverse moments of the eigenvalues are expected. We evaluate explicitly the pertinent microscopic spectral density, and found it in agreement with numerical calculations. We suggest that similar sum rules are of relevance to QCD at the critical temperature, and even above if the transition is amenable to a Landau-Ginzburg description.

hep-ph↗