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We present a scaling hypothesis for the distribution function of the shortest paths connecting any two points on a percolating cluster which accounts for {\it (i)} the effect of the finite size of the system, and {\it (ii)} the dependence…

Multifractal scaling analysis of nuclear giant resonance transition probability distributions is performed within the approximation which takes into account the one-particle-one-hole (1p-1h) and 2p-2h states. A new measure to determine the…

We investigate the sandpile model with Yukawa-type interactions, whose effective range is tuned by an external parameter $R$. Our results reveal that at specific values of $R$, the system exhibits giant avalanches that span the system,…

We study a large class of Bernoulli percolation models on random lattices of the half- plane, obtained as local limits of uniform planar triangulations or quadrangulations. We first compute the exact value of the site percolation threshold…

Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry, is believed to be dual to a scalar theory with a global U(1) symmetry, near the phase transition point. The conjectured duality leads to definite predictions for…

In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL) which is a multi-multifractal and whose dual is a scale-free network. The characteristic properties of percolation is that it…

Considering a "random walk in a random environment" in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization"…

We consider independent and $m$-dependent two-dimensional oriented site percolation with open-site density close to one started from Bernoulli product measures. We show that the probability of an occupied interval in the former process…

In a recent Letter Simon and Lee suggested a scaling law for thermodynamic and kinetic properties of superconductors with lines of gap nodes. However their crossover parameter between the bulk dominated regime and the vortex dominated…

We study the anomalous transport in systems of random walks (RW's) on comb-like lattices with fractal sidebranches, showing subdiffusion, and in a system of Brownian particles driven by a random shear along the x-direction, showing a…

We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same…

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…

In this paper, we consider accessibility percolation on hypercubes, i.e., we place i.i.d. uniform [0,1] random variables on vertices of a hypercube, and study whether there is a path connecting two vertices such that the values of these…

The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…

We report on the exact treatment of a random-matrix representation of bond percolation model on a square lattice in two dimensions with occupation probability $p$. The percolation problem is mapped onto a random complex matrix composed of…

We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find…

An exact formula is given for the probability that there exists a spanning cluster between opposite boundaries of an annulus, in the scaling limit of critical percolation. The entire distribution function for the number of distinct spanning…

Controlled experimental studies of percolation are challenging due to difficulties in tuning site connectivity, isolating local interactions, and mitigating finite-size effects. In this work, we experimentally investigate percolation with a…

Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…

We investigate the description of current transfer in polycrystalline superconductors by percolation theory and its limitations. Various computer models that have been proposed are reviewed and related to the experimental and theoretical…