Related papers: Phase transition on randomly horizontally stretche…

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…

Let $G_{n,p}^1$ be a superposition of the random graph $G_{n,p}$ and a one-dimensional lattice: the $n$ vertices are set to be on a ring with fixed edges between the consecutive vertices, and with random independent edges given with…

Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…

We present some exact results on bond percolation. We derive a relation that specifies the consequences for bond percolation quantities of replacing each bond of a lattice $\Lambda$ by $\ell$ bonds connecting the same adjacent vertices,…

We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…

A percolation model is proposed to explain the structural phase transitions found in Li$_{1-x}$H$_x$IO$_3$ mixed crystals as a function of the concentration parameter $x$. The percolation thresholds are obtained from Monte Carlo simulations…

The ranges of transmission of the mobiles in a Mobile Ad-hoc Network are not uniform in reality. They are affected by the temperature fluctuation in air, obstruction due to the solid objects, even the humidity difference in the environment,…

We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of Z^2 are independently occupied with small probability p,…

We consider the first passage percolation model on the square lattice. In this model, $\{t(e): e{an edge of}{\bf Z}^2 \}$ is an independent identically distributed family with a common distribution $F$. We denote by $T({\bf 0}, v)$ the…

We investigate the problem of percolation of words in a random environment. To each vertex, we independently assign a letter $0$ or $1$ according to Bernoulli r.v.'s with parameter $p$. The environment is the resulting graph obtained from…

We consider the first passage percolation model on the square lattice with an edge weight distribution F. In this paper, we consider the number of optimal paths for two points separated by a long distance. We show that there is a phase…

We give the exact critical frontier of the Potts model on bowtie lattices. For the case of $q=1$, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff…

We study the bond percolation game and the site percolation game on the rooted Galton-Watson tree $T_{\chi}$ with offspring distribution $\chi$. We obtain the probabilities of win, loss and draw for each player in terms of the fixed points…

The social percolation model \citep{solomon-et-00} considers a 2-dimensional regular lattice. Each site is occupied by an agent with a preference $x_{i}$ sampled from a uniform distribution $U[0,1]$. Agents transfer the information about…

In the random $r$-neighbour bootstrap percolation process on a graph $G$, a set of initially infected vertices is chosen at random by retaining each vertex of $G$ independently with probability $p\in (0,1)$, and "healthy" vertices get…

We study the contact process on spatially embedded networks, consisting of a regular square lattice with long-range connections. To generate the networks, a long-range connection is randomly added to each node $i$ of a square lattice,…

We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a…

We conducted Monte Carlo simulations to analyze the percolation transition of a non-symmetric loop model on a regular three-dimensional lattice. We calculated the critical exponents for the percolation transition of this model. The…

In Poisson percolation each edge becomes open after an independent exponentially distributed time with rate that decreases in the distance from the origin. As a sequel to our work on the square lattice, we describe the limiting shape of the…

We study percolation on the hierarchical lattice of order $N$ where the probability of connection between two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)},\; \delta >-1$. Since the distance is an ultrametric, there…