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The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…
A large peculiar velocity of the intergalactic medium produces a Doppler shift of the cosmic microwave background with a frequency-dependent quadrupole term. This quadrupole will act as a source for polarization of the cosmic microwave…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…
We study the transport properties of directed percolation clusters at the upper critical dimension $d_{c} = 4+1$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) scaling behavior. Employing field…
We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For…
We investigate percolation in the Boolean model with convex grains in high dimension. For each dimension d, one fixes a compact, convex and symmetric set K $\subset$ R d with non empty interior. In a first setting, the Boolean model is a…
We consider the Poisson Boolean percolation model in $\mathbb{R}^2$, where the radii of each ball is independently chosen according to some probability measure with finite second moment. For this model, we show that the two thresholds, for…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
We examine the regime between crystalline and amorphous packings of anisotropic objects on surfaces of different genus by continuously varying their size distribution or shape from monodispersed spheres to bidispersed mixtures or…
Scaling theory predicts complete localization in $d=2$ in quantum systems belonging to orthogonal class (i.e. with time-reversal symmetry and spin-rotation symmetry). The conductance $g$ behaves as $g \sim exp(-L/l)$ with system size $L$…
Place an obstacle with probability $1-p$ independently at each vertex of $\mathbb Z^d$, and run a simple random walk until hitting one of the obstacles. For $d\geq 2$ and $p$ strictly above the critical threshold for site percolation, we…
The arboreal gas is the probability measure on (unrooted spanning) forests of a graph in which each forest is weighted by a factor $\beta>0$ per edge. It arises as the $q\to 0$ limit of the $q$-state random cluster model with $p=\beta q$.…
A local order parameter which is important in the analysis of phase transitions in frustrated combinatorial problems is the probability that a node is frozen in a particular state. There is a percolative transition when an infinite…
Spontaneous strain localization occurs during mechanical tests of a model amorphous solid simulated using molecular dynamics. The degree of localization depends upon the extent of structural relaxation prior to mechanical testing. In the…
An analysis of water clustering is used to study the quasi-2D percolation transition of water adsorbed at planar hydrophilic surfaces. Above the critical temperature of the layering transition (quasi-2D liquid-vapor phase transition of…
We combine percolation theory and Monte Carlo simulation to study in two dimensions the connectivity of an equilibrium lattice model of interacting Janus disks which self-assemble into an orientationally ordered stripe phase at low…
Consider an independent site percolation model on $\Z^d,\ d\geq 2$, with parameter $p \in (0,1)$, where there are only nearest neighbor bonds and long range bonds of length $k$ parallel to some coordinate axis. We show that the percolation…
Consider an independent site percolation model with parameter $p \in (0,1)$ on $\Z^d,\ d\geq 2$ where there are only nearest neighbor bonds and long range bonds of length $k$ parallel to each coordinate axis. We show that the percolation…
We study the phase transition of the three-dimensional complex |psi|^4 theory by considering the geometrically defined vortex-loop network as well as the magnetic properties of the system in the vicinity of the critical point. Using…
We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence…