相关论文: Directed percolation with an absorbing boundary
We identify the asymptotic distribution of the chemical distance in high-dimensional critical Bernoulli percolation. Namely, we show that the distance between the origin and a distant vertex conditioned to lie in the cluster of the origin…
In the context of percolation in a regular tree, we study the size of the largest cluster and the length of the longest run starting within the first d generations. As d tends to infinity, we prove almost sure and weak convergence results.
We consider the model of a directed polymer in a random environment defined on the infinite cluster of supercritical Bernoulli bond percolation in dimensions $d \geq 3$. For this model, it was proved in arXiv:2205.06206 that for almost…
We report on universality in boundary domain growth in cluster aggregation in the limit of maximum concentration. Maximal concentration means that the diffusivity of the clusters is effectively zero and, instead, clusters merge successively…
Absorbing phase transition in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken…
We consider the fractal dimensions d_k of the k-connected part of percolation clusters in two dimensions, generalizing the cluster (k=1) and backbone (k=2) dimensions. The codimensions X_k = 2-d_k describe the asymptotic decay of the…
We investigate a model of epidemic spreading with partial immunization which is controlled by two probabilities, namely, for first infections, $p_0$, and reinfections, $p$. When the two probabilities are equal, the model reduces to directed…
We study, on a square lattice, an extension to fully coordinated percolation which we call iterated fully coordinated percolation. In fully coordinated percolation, sites become occupied if all four of its nearest neighbors are also…
We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, \textbf{87} 052107 (2013)],…
The percolation behaviour during the deposit formation, when the spanning cluster was formed in the substrate plane, was studied. Two competitive or mixed models of surface layer formation were considered in (1+1)-dimensional geometry.…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
We consider a directed random walk on the backbone of the supercritical oriented percolation cluster in dimensions $d+1$ with $d \ge 3$ being the spatial dimension. For this random walk we prove an annealed local central limit theorem and a…
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
We consider a directed percolation process on an ${\cal M}$ x ${\cal N}$ rectangular lattice whose vertical edges are directed upward with an occupation probability y and horizontal edges directed toward the right with occupation…
The results of investigations of main characteristics of a one-dimensional percolation theory (percolation threshold, critical exponents of correlation radius and specific heat, and free energy) are presented for the problem of bonds and…
The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in $d \ge 2$ dimensions. Salient features of the phase diagram are established in each case. The models are based on site…
We consider directed percolation processes for particle types A and B coupled unidirectionally by a transmutation reaction A -> B. It is shown that the strong coupling regime of this recently introduced problem defines a universality class…
We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x'$, and subsequently take the limit as $|x|$, $|x'|$ as well as $|x-x'|$ diverge to infinity.…
Percolation theory is usually applied to lattices with a uniform probability p that a site is occupied or that a bond is closed. The more general case, where p is a function of the position x, has received less attention. Previous studies…
In two dimensions, the average electrical conductance from a point in a percolating network to the network boundary should be related by a conformal transformation to the conductance from one point to another in an unbounded network. We…