Weak convergence of Vervaat and Vervaat Error processes of long-range dependent sequences

Following Cs\"{o}rg\H{o}, Szyszkowicz and Wang (Ann. Statist. {\bf 34}, (2006), 1013--1044) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes, extending their results to distributions with unbounded support and removing normality assumption

Reduction principles for quantile and Bahadur-Kiefer processes of long-range dependent linear sequences

In this paper we consider quantile and Bahadur-Kiefer processes for long range dependent linear sequences. These processes, unlike in previous studies, are considered on the whole interval $(0,1)$. As it is well-known, quantile processes can have very erratic behavior on the tails. We overcome this problem by considering these processes with appropriate weight functions. In this way we conclude strong approximations that yield some remarkable phenomena that are not shared with i.i.d. sequences, including weak convergence of the Bahadur-Kiefer processes, a different pointwise behavior of the general and uniform Bahadur-Kiefer processes, and a somewhat "strange" behavior of the general quantile process.Comment: Preprint. The final version will appear in Probability Theory and Related Field

Lepton interferometry in relativistic heavy ion collisions - a case study

We propose intensity interferometry with identical lepton pairs as an efficient tool for the estimation of the source size of the expanding hot zone produced in relativistic heavy ion collisions. This can act as a complementary method to two photon interferometry. The correlation function of two electrons with the same helicity has been evaluated for RHIC energies. The thermal shift of the rho meson mass has negligible effects on the HBT radii.Comment: 5 pages and 2 figure

Reduced-bias estimator of the Conditional Tail Expectation of heavy-tailed distributions

International audienceSeveral risk measures have been proposed in the literature. In this paper, we focus on the estimation of the Conditional Tail Expectation (CTE). Its asymptotic normality has been first established in the literature under the classical assumption that the second moment of the loss variable is finite, this condition being very restrictive in practical applications. Such a result has been extended by Necir {\it et al.} (2010) in the case of infinite second moment. In this framework, we propose a reduced-bias estimator of the CTE. We illustrate the efficiency of our approach on a small simulation study and a real data analysis

Modified Boltzmann Transport Equation and Freeze Out

We study Freeze Out process in high energy heavy ion reaction. The description of the process is based on the Boltzmann Transport Equation (BTE). We point out the basic limitations of the BTE approach and introduce Modified BTE. The Freeze Out dynamics is presented in the 4-dimensional space-time in a layer of finite thickness, and we employ Modified BTE for the realistic Freeze Out description.Comment: 9 pages, 2 figure

Low Freeze-out Temperature and High Collective Velocities in Relativistic Heavy-Ion Collisions

On the basis of a nine-parameter expanding source model that includes special relativity, quantum statistics, resonance decays, and freeze-out on a realistic hypersurface in spacetime, we analyze in detail invariant pi+, pi-, K+, and K- one-particle multiplicity distributions and pi+ and K+ two-particle correlations in nearly central collisions of Si + Au at a laboratory bombarding energy per nucleon of 14.6 GeV/c. By considering separately the one-particle data and the correlation data, we find that the central baryon density, nuclear temperature, transverse collective velocity, longitudinal collective velocity, and source velocity are determined primarily by one-particle multiplicity distributions and that the transverse radius, longitudinal proper time, width in proper time, and pion incoherence fraction are determined primarily by two-particle correlations. By considering separately the pion data and the kaon data, we find that although the pion freeze-out occurs somewhat later than the kaon freeze-out, the 99% confidence-level error bars associated with the two freeze-outs overlap. These and other detailed studies confirm our earlier conclusion based on the simultaneous consideration of the pion and kaon one-particle and correlation data that the freeze-out temperature is less than 100 MeV and that both the longitudinal and transverse collective velocities--which are anti-correlated with the temperature--are substantial. We also discuss the flaws in several previous analyses that yielded a much higher freeze-out temperature of approximately 140 MeV for both this reaction and other reactions involving heavier projectiles and/or higher bombarding energies.Comment: 14 pages. RevTeX 3.1. Submitted to Physical Review C. PostScript version available at http://t2.lanl.gov/publications/publications.html or at ftp://t2.lanl.gov/pub/publications/lf

Resonance contributions to HBT correlation radii

We study the effect of resonance decays on intensity interferometry for heavy ion collisions. Collective expansion of the source leads to a dependence of the two-particle correlation function on the pair momentum K. This opens the possibility to reconstruct the dynamics of the source from the K-dependence of the measured HBT radii. Here we address the question to what extent resonance decays can fake such a flow signal. Within a simple parametrization for the emission function we present a comprehensive analysis of the interplay of flow and resonance decays on the one- and two-particle spectra. We discuss in detail the non-Gaussian features of the correlation function introduced by long-lived resonances and the resulting problems in extracting meaningful HBT radii. We propose to define them in terms of the second order q-moments of the correlator C(q, K). We show that this yields a more reliable characterisation of the correlator in terms of its width and the correlation strength `lambda' than other commonly used fit procedures. The normalized fourth-order q-moments (kurtosis) provide a quantitative measure for the non-Gaussian features of the correlator. At least for the class of models studied here, the kurtosis helps separating effects from expansion flow and resonance decays, and provides the cleanest signal to distinguish between scenarios with and without transverse flow.Comment: 23 pages, twocolumn RevTeX, 12 eps-figures included, minor changes following referee comment

Fluctuations of the Initial Conditions and the Continuous Emission in Hydrodynamic Description of Two-Pion Interferometry

Within hydrodynamic approach, we study the Bose-Einstein correlation of identical pions by taking into account both event-by-event fluctuating initial conditions and continuous pion emission during the whole development of the hot and dense matter formed in high-energy collisions. Considerable deviations occur, compared to the usual hydro calculations with smooth initial conditions and a sudden freeze-out on a well defined hypersurface. Comparison with data at RHIC shows that, despite rather rough approximation we used here, this description can give account of the $m_T$ dependence of $R_L$ and $R_s$ and improves considerably the one for $R_o$ with respect to the usual version.Comment: 5 pages, 4 figure

Quark-Gluon Plasma Fireball

Lattice-QCD results provide an opportunity to model, and extrapolate to finite baryon density, the properties of the quark-gluon plasma (QGP). Upon fixing the scale of the thermal coupling constant and vacuum energy to the lattice data, the properties of resulting QGP equations of state (EoS) are developed. We show that the physical properties of the dense matter fireball formed in heavy ion collision experiments at CERN-SPS are well described by the QGP-EoS we presented. We also estimate the properties of the fireball formed in early stages of nuclear collision, and argue that QGP formation must be expected down to 40A GeV in central Pb--Pb interactions.Comment: 10 pages, 9 postscript figures, 1 table, uses revtex, V3: introduced difference between n_f and n_s; fireball restframe energy corrected, references added. Publisched version in press Phys. Rev.

Two-Particle Correlations in Relativistic Heavy-Ion Collisions

Two-particle momentum correlations between pairs of identical particles produced in relativistic heavy-ion reactions can be analyzed to extract the space-time structure of the collision fireball. We review recent progress in the application of this method, based on newly developed theoretical tools and new high-quality data from heavy-ion collision experiments. Implications for our understanding of the collision dynamics and for the search for the quark-gluon plasma are discussed.Comment: 44 pages, LaTeX, 11 Figures, uses special style files (included), prepared for Ann. Rev. Nucl. Part. Sci. 49 (1999). Error in Chapt. 1 corrected and a few references adde