Questions concerning the properties and quantification of density fluctuations in point patterns continue to provide many theoretical challenges. The purpose of this paper is to characterize certain fundamental aspects of local density fluctuations associated with general point patterns in any space dimension d. Our specific objectives are to study the variance in the number of points contained...

We study self-avoiding random walks in an environment where sites are excluded randomly, in two and three dimensions. For a single polymer chain, we study the statistics of the time averaged monomer density and show that these are well described by multifractal statistics. This is true even far from the percolation transition of the disordered medium. We investigate solutions of chains in a dis...

We use molecular dynamics simulations of the SPC-E model of liquid water to derive probability distributions for water density fluctuations in probe volumes of different shapes and sizes, both in the bulk as well as near hydrophobic and hydrophilic surfaces. Our results are obtained with a biased sampling of coarse-grained densities that is easily combined with molecular dynamics integration al...

b We discuss the baryon-number susceptibility χ B and related topics which include the density fluctuations around the critical point of the chiral transition at finite temperature T and baryon density ρ B. Phenomenological implications of the density fluctuations near the first-order chiral transition at finite density are also discussed.

In this article measurements of small scale electron density fluctuations in dithering high confinement ~H!-mode plasmas obtained by collective scattering of infrared light are presented. A scan of the fluctuation wavenumber was made in a series of similar discharges in the Wendelstein 7-AS ~W7-AS! stellarator @H. Renner et al., Plasma Phys. Control. Fusion 31, 1579 ~1989!#. The experimental se...

We present a brief introduction to the statistical properties of systems with large fluctuations. We point out that for such systems the relevant statistical quantities are scaling exponents and the nature of fluctuations is completely different from the one belonging to system with small fluctuations. We then propose two test to be performed on galaxy counts data as a function of apparent magn...

In the study of the evolution of the universe, it is important to understand the origin of the cosmic density fluctuations. The most conventional scenario is inflation [1] where quantum fluctuation of the inflaton field during the inflation becomes the origin of the cosmic density fluctuations. From the particle-physics point of view, it is desirable to construct a model of inflation which is t...