Correlations and fluctuations in hardonic multiciplicity distribution: The meaning of KNO scaling

Carruthers, Peter; Shih, Chia C.

doi:10.1016/0370-2693(83)90884-5

Cited by 140 publications

(32 citation statements)

References 19 publications

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“…The final model we consider has had a colorful history. The negative binomial distribution, also known as the modified Bose-Einstein distribution, was used early on by Carruthers & Shih (1983) to study the count distribution of charged hadrons resulting from high-energy collisions and by Carruthers & Duong-van (1983) to describe the observed distribution of Zwicky clusters. The model can be described by:…”

Section: Hierarchical Modelsmentioning

confidence: 99%

The DEEP2 Galaxy Redshift Survey: The Evolution of Void Statistics fromz∼ 1 toz∼ 0

Conroy

Coil

White

et al. 2005

ApJ

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We present measurements of the void probability function (VPF) at z ∼ 1 using data from the DEEP2 Redshift Survey and its evolution to z ∼ 0 using data from the Sloan Digital Sky Survey (SDSS). We measure the VPF as a function of galaxy color and luminosity in both surveys and find that it mimics trends displayed in the two-point correlation function, ξ; namely that samples of brighter, red galaxies have larger voids (i.e. are more strongly clustered) than fainter, blue galaxies. We also clearly detect evolution in the VPF with cosmic time, with voids being larger in comoving units at z ∼ 0. We find that the reduced VPF matches the predictions of a 'negative binomial' model for galaxies of all colors, luminosities, and redshifts studied. This model lacks a physical motivation, but produces a simple analytic prediction for sources of any number density and integrated two-point correlation function,ξ. This implies that differences in the VPF across different galaxy populations are consistent with being due entirely to differences in the population number density andξ. We compare the VPF at z ∼ 1 to N -body ΛCDM simulations and find good agreement between the DEEP2 data and mock galaxy catalogs. Interestingly, we find that the dark matter particle reduced VPF follows the physically motivated 'thermodynamic' model, while the dark matter halo reduced VPF more closely follows the negative binomial model. The robust result that all galaxy populations follow the negative binomial model appears to be due to primarily to the clustering of dark matter halos. The reduced VPF is insensitive to changes in the parameters of the halo occupation distribution, in the sense that halo models with the sameξ will produce the same VPF. For the wide range of galaxies studied, the VPF therefore does not appear to provide useful constraints on galaxy evolution models that cannot be gleaned from studies ofξ alone.

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Section: Hierarchical Modelsmentioning

confidence: 99%

The DEEP2 Galaxy Redshift Survey: The Evolution of Void Statistics fromz∼ 1 toz∼ 0

Conroy

Coil

White

et al. 2005

ApJ

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“…The Negative Binomial (hereafter NB) process is a discrete valued process commonly used when the empirical count data exhibit overdispersion, that is, when the sample variance is larger than the sample mean, in many different fields, such as particle physics ( [12,15]) and cosmology ( [11]). It can be defined, alternatively, as a compound Poisson process with logarithmic jumps or as a mixed Poisson process (i.e., a Poisson process subordinated to an independent Gamma subordinator, see, e.g., [28]).…”

Section: Downloaded By [Unsw Library] At 19:46 10 August 2015mentioning

confidence: 99%

Fractional Gamma and Gamma-Subordinated Processes

Beghin

2015

Stochastic Analysis and Applications

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We introduce and study fractional generalizations of the well-known Gamma process, in the following sense: the corresponding densities are proved to satisfy the same differential equation as the usual Gamma process, but with the shift operator replaced by its fractional version of order $\nu >0$. In the case $\nu >1$, the solution corresponds to the density of a Gamma process time-changed by an independent stable subordinator of index $1/\nu $. For $\nu $ less than one an analogous result holds, with the subordinator replaced by the inverse. In this case the fractional Gamma process is proved to be a non-stationary version of the standard one, with power law behavior of the expected value. Hence it can be considered a useful tool in modelling stochastic deterioration in the non-linear cases, a situation which often occurs in real data (see i.e., \cite{VAN} and the references therein).\ud As a consequence of the previous results, the fractional generalizations of some Gamma subordinated processes (i.e. the Variance Gamma, the Geometric Stable and the Negative Binomial) are introduced and the corresponding fractional differential equations are obtained. These processes are particularly relevant for a wide range of financial and technological applications

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“…Comparison with N-body simulations indicate that the geometric hierarchical (GH, e.g. Carruthers & Shih 1983) and negative binomial (NB, e.g. Hamilton 1988) models are good approximation for galaxies (sub-haloes) and haloes extracted from N-body simulations, respectively (Fry & Colombi 2013).…”

Section: Hierarchical Scaling and Random Dilutionsmentioning

confidence: 99%

Ultraviolet background fluctuations with clustered sources

Desjacques

Dizgah

Biagetti

2014

Monthly Notices of the Royal Astronomical Society

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We develop a count-in-cells approach to the distribution of ultraviolet background fluctuations that includes source clustering. We demonstrate that an exact expression can be obtained if the clustering of ionising sources follows the hierarchical ansatz. In this case, the intensity distribution depends solely on their 2-point correlation function. We show that the void scaling function of high redshift mock quasars is consistent with the Negative Binomial form, before applying our formalism to the description of HeII-ionising fluctuations at the end of helium reionization. The model inputs are the observed quasar luminosity function and 2-point correlation at z ∼ 3. We find that, for an (comoving) attenuation length 55 Mpc, quasar clustering contributes less than 30% of the variance of intensity fluctuations so long as the quasar correlation length does not exceed ∼ 15 Mpc. We investigate also the dependence of the intensity distribution on the large-scale environment. Differences in the mean HeII-ionising intensity between low-and high-density regions could be a factor of few if the sources are highly clustered. An accurate description of quasar demographics and their correlation with strong absorption systems is required to make more precise predictions. Recently, Dixon, Furlanetto & Mesinger (2014) have addressed the impact of quasar clustering using a seminumeric method, in which dark matter haloes are identified in realisations of the linear density field using the excursion set approach. They have found a relatively weak effect. However, given the current uncertainties on the demographics of high redshift quasars, it would be desirable to revisit this issue and explore a wider spectrum of quasar clustering amplitudes.In this paper, we will investigate this issue analytically c 0000 RAS

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Correlations and fluctuations in hardonic multiciplicity distribution: The meaning of KNO scaling

Cited by 140 publications

References 19 publications

The DEEP2 Galaxy Redshift Survey: The Evolution of Void Statistics fromz∼ 1 toz∼ 0

The DEEP2 Galaxy Redshift Survey: The Evolution of Void Statistics fromz∼ 1 toz∼ 0

Fractional Gamma and Gamma-Subordinated Processes

Ultraviolet background fluctuations with clustered sources

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