Abstract:
We construct the hadronic multiplicity distribution in terms of an elementary distribution (at given impact parameter) and the inelastic overlap function characterized by the observed BEL (Blacker-Edgier-Larger) behaviour. With suitable parametrizations for the elementary quantities, based on some geometrical arguments and the most recent data on e+e- annihilation, an excellent description of pp and p(bar)p inelastic multiplicity distributions at the highest energies is obtained.

Abstract:
Preliminary results on local multiplicity fluctuations in hadronic Z decays are presented. The data were obtained using the L3 detector at LEP. It is investigated to what extent Monte-Carlo models, which are tuned to reproduce global event-shape variables and single-particle inclusive distributions, can describe the local fluctuations measured by means of bunching parameters.

Abstract:
The charged-particle multiplicity distribution is measured for all hadronic events as well as for light-quark and b-quark events produced in e+e- collisions at the Z pole. Moments of the charged-particle multiplicity distributions are calculated. The H moments of the multiplicity distributions are studied, and their quasi-oscillations as a function of the rank of the moment are investigated.

Abstract:
The possibility to relate multiplicity distributions and their moments, as measured in the hadronic final state in e(+)e(-) annihilation, to features of the initial partonic state is analyzed from a theoretical and phenomenological point of view. Recent developments on the subject are discussed.

Abstract:
Multiplicity distributions of neutral and charged particles arising from squeezed coherent states are investigated. Projections onto global isospin states are considered. We show how a small amount of squeezing can significantly change the multiplicity distributions. The formalism is proposed to describe the phenomenological properties of neutral and charged particles anomalously produced in hadronic and nuclear collisions at very high energies.

Abstract:
I examine the phenomenology of particle multiplicity distributions, with special emphasis on the low multiplicities that are a background in the study of rapidity gaps. In particular, I analyze the multiplicity distribution in a rapidity interval between two jets, using the HERWIG QCD simulation with some necessary modifications. The distribution is not of the negative binomial form, and displays an anomalous enhancement at zero multiplicity. Some useful mathematical tools for working with multiplicity distributions are presented. It is demonstrated that ignoring particles with pt<0.2 has theoretical advantages, in addition to being convenient experimentally.

Abstract:
Quantum chromodymamics (QCD) approach to the problem of multiplicity distributions in high energy particle collisions is described. The solutions of QCD equations for generating functions of the multiplicity distributions in gluon and quark jets are presented for both fixed and running coupling constants. The newly found characteristics very sensitive to distribution shapes is discussed. The predictions are confronted to experimental data. Evolution of the multiplicity distributions with decreasing phase space windows is considered and discussed in connection to the notions of intermittency and fractality. Some other QCD effects are briefly described.

Abstract:
The solution of QCD equations for generating functions of {\it parton} multiplicity distributions reveals new peculiar features of cumulant moments oscillating as functions of their rank. It happens that experimental data on {\it hadron} multiplicity distributions in $e^{+}e^{-}, hh, AA$ collisions possess the similar features. However, the "more regular" models like $\lambda \phi ^3$ behave in a different way. Evolution of the moments at smaller phase space bins and zeros of the truncated generating functions are briefly discussed.

Abstract:
Moment analysis of global multiplicity distribution previously done for $e^{+}e^{-}$ and $hh$ processes is applied to $hA$ and $AA$ collisions. The oscillations of cumulants as functions of their rank are found in all the cases. Some phenomenological approaches and quark-gluon string models are confronted to experimental data. It has been shown that the analysis is a powerful tool for revealing the tiny features of the distributions, and its qualitative results in various processes are rather stable for different multiplicity cut-offs determined by experimental (or Monte-Carlo) statistics.

Abstract:
The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand canonical partition function. Taylor expansion of the generating function is used to separate contributions to the partition function in their power in volume. We employ Laplace's asymptotic expansion to show that any equilibrium distribution of multiplicity, charge, energy, etc. tends to a multivariate normal distribution in the thermodynamic limit. Gram-Charlier expansion allows additionally for calculation of finite volume corrections. Analytical formulas are presented for inclusion of resonance decay and finite acceptance effects directly into the system partition function. This paper consolidates and extends previously published results of current investigation into properties of statistical ensembles.