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We review the problem of fluctuations in particle shower theory. By using a generalization of Furry equation, we find relations between the $n$--particle correlation function and the number of particles average or 1--particle correlation…
Approximate expressions for correlation functions in binary inhomogeneous mixtures are derived in a framework of the mesoscopic theory [Ciach A., Mol. Phys., 2011, {\textbf{109}}, 1101]. Fluctuation contribution is taken into account in a…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
Complete spectroscopy (measurements of a complete sequence of consecutive levels) is often considered as a prerequisite to extract fluctuation properties of spectra. It is shown how this goal can be achieved even if only a fraction of…
Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…
Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…
Enhanced fluctuations and correlations have been observed in the phase transitions of many systems. Their appearance at the predicted QCD phase transition (especially near the expected critical point) may provide insight into the nature of…
The link between the scaling function extracted from the analysis of (e,e') cross sections and the spectral function/momentum distribution in nuclei is revisited. Several descriptions of the spectral function based on the independent…
We study the statistical fluctuations (such as the variance) of causal set quantities, with particular focus on the causal set action. To facilitate calculating such fluctuations, we develop tools to account for correlations between causal…
The observation of scaling in processes in which a weakly interacting probe delivers large momentum ${\bf q}$ to a many-body system simply reflects the dominance of incoherent scattering off target constituents. While a suitably defined…
We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show for an equilibrium liquid that this function is related to fluctuations in a bulk…
We present a conformal theory for intermittent scalar fields. As an example, we consider the energy flux from large to small scales in the developed turbulent flow. The conformal correlation functions are found in the inertial range of…
We study the polarization-temperature correlations on the cosmic microwave sky resulting from an initial scale invariant spectrum of tensor (gravity wave) fluctuations, such as those which might arise during inflation. The correlation…
We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling…
The Interplanetary Magnetic Field shows complex spatial and temporal variations. Single spacecraft measurements reveal only a one dimensional section of this rich four dimensional phenomenon. Multi-point measurements of the four Cluster…
An approach is suggested for treating multiscale fluctuations in macromolecular systems. The emphasis is on the statistical properties of such fluctuations. The approach is illustrated by a macromolecular system with mesoscopic fluctuations…
The autocorrelation function of spectral determinants is proposed as a convenient tool for the characterization of spectral statistics in general, and for the study of the intimate link between quantum chaos and random matrix theory, in…
There often appear coherently oscillating scalar fields in particle physics motivated cosmological scenarios, which may have rich phenomenological consequences. Scalar fields should somehow interact with background thermal bath in order to…
Occupation probabilities for primary-secondary-primary cell strings and correlation functions for primary sites of a decorated lattice model are expressed through the well-studied partition function and correlation functions of the Ising…
Standard results for the fluctuations of thermodynamic quantities are derived under the assumption of sampling identical systems that are in different, not fully equilibrated states. These results apply to fluctuations with time in a…