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The most common statistic used to analyze large-scale structure surveys is the correlation function, or power spectrum. Here, we show how `slicing' the correlation function on local density brings sensitivity to interesting non-Gaussian…
We have used integral two-point spatial correlation function and its second derivative to analyze the distribution of quasars in three very deep surveys published in the literature. Statistically significant ($\sim 2-3\sigma $) correlations…
We compute the entanglement between separated blocks in certain spin models showing that at criticality this entanglement is a function of the ratio of the separation to the length of the blocks and can be written as a product of a power…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
We examine the Detrended Fluctuation Analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling that appear at small time scales become stronger in…
The functionality of nodes in a network is often described by the structural feature of belonging to the giant component. However, when dealing with problems like transport, a more appropriate functionality criterion is for a node to belong…
We present a new view of Feynman diagrams for the field theory of transport on percolation clusters. The diagrams for random resistor networks are interpreted as being resistor networks themselves. This simplifies the field theory…
We consider oriented percolation on Z^d times Z_+ whose bond-occupation probability is pD(...), where p is the percolation parameter and D is a probability distribution on Z^d. Suppose that D(x) decays as |x|^{-d-\alpha} for some \alpha>0.…
It is well know that systems with an interaction decaying as a power of the distance may have critical exponents that are different from those of short-range systems. The boundary between long-range and short-range is known, however the…
This paper presents a Monte-Carlo study of percolation in a distorted square lattice, in which, the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable…
We study the topological properties of functional connectivity patterns among cortical areas in the frequency domain. The cortical networks were estimated from high-resolution EEG recordings in a group of spinal cord injured patients and in…
This work is the first in a series of papers devoted to the construction and study of scaling limits of dynamical and near-critical planar percolation and related objects like invasion percolation and the Minimal Spanning Tree. We show here…
The BTW sandpile model is considered on three dimensional percolation lattice which is tunned with the occupation parameter $p$. Along with the three-dimensional avalanches, we study the energy propagation in two-dimensional cross-sections.…
The effects of long- and short-range correlations on the charge distributions of some medium and heavy nuclei are investigated. The long-range correlations are treated within the Random Phase Approximation framework and the short-range…
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Based on the idea from general fractals and scaling,…
Although both RNA and proteins have densely packed native structures, chain organizations of these two biopolymers are fundamentally different. Motivated by the recent discoveries in chromatin folding that interphase chromosomes have…
We study the correlations of the celebrated Sine$_\beta$ point process. This point process arises as the bulk scaling limit of $\beta$-ensembles and has a geometric description through the Brownian carousel, as shown by Valk\'o and Vir\'ag…
The average matter density within the turnaround scale, which demarcates where galaxies shift from clustering around a structure to joining the expansion of the Universe, is an important cosmological probe. However, a measurement of the…
We develop the skeleton algorithm to define the number of main branches $N_b$ of diffusion-limited aggregation (DLA) clusters. The skeleton algorithm provides a systematic way to remove dangling side branches of the DLA cluster and has…
We consider a percolation model on square lattices with sites weighted by beta-distributed random variables $S\sim \mathrm{Beta}(a,b)$ with a positive real parameters $a>0$ and $b>0$. Using the Monte Carlo method, we estimate the…