相关论文: On the effect of adding epsilon-Bernoulli percolat…
Employing a conformal map to hyperbolic space cross a circle, we compute the universal contribution to the vacuum entanglement entropy (EE) across a sphere in even-dimensional conformal field theory. Previous attempts to derive the EE in…
The aim of this paper is to explore possible ways of extending Smirnov's proof of Cardy's formula for critical site-percolation on the triangular lattice to other cases (such as bond-percolation on the square lattice); the main question we…
We answer a question of Benjamini and Schramm by proving that under reasonable conditions, quotienting a graph strictly increases the value of its percolation critical parameter $p_c$. More precisely, let $\mathcal{G}=(V,E)$ be a…
In the present article, numerical simulations have been performed to find the bond and site percolation thresholds on two-dimensional Gabriel graphs (GG) for Poisson point processes. GGs belong to the family of proximity graphs and are…
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…
We present simulations of a 3-d percolation model studied recently by K.J. Schrenk et al. [Phys. Rev. Lett. 116, 055701 (2016)], obtained with a new and more efficient algorithm. They confirm most of their results in spite of larger systems…
An elegant bootstrap percolation result on the hyperrectangle graph was proved by Balogh, Bollob\'as, Morris, and Riordan using a linear algebric method in 2012. This paper studies the same problem by purely combinatorial means. The base…
Let $Q^d$ be the $d$-dimensional binary hypercube. We form a random subgraph $Q^d_p\subseteq Q^d$ by retaining each edge of $Q^d$ independently with probability $p$. We show that, for every constant $\varepsilon>0$, there exists a constant…
We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
We exploit a connection between distances in the infinite percolation cluster, when the parameter is close to one, and the discrete-time TASEP on $\mathbb{Z}$. This shows that when the parameter goes to one, large balls in the cluster are…
Let $d\ge 3$ be a fixed integer. Let $y:= y(p)$ be the probability that the root of an infinite $d$-regular tree belongs to an infinite cluster after $p$-bond-percolation. We show that for every constants $b,\alpha>0$ and $1<\lambda< d-1$,…
Consider Bernoulli bond percolation on a graph nicely embedded in hyperbolic space $\mathbb H^d$ in such a way that it admits a transitive action by isometries of $\mathbb H^d$. Let $p_0$ be the supremum of such percolation parameters that…
Percolation on a plane is usually associated with clusters spanning two opposite sides of a rectangular system. Here we investigate three-leg clusters generated on a square lattice and spanning the three sides of equilateral triangles. If…
Benjamini and Kesten introduced in 1995 the problem of embedding infinite binary sequences into a Bernoulli percolation configuration, known as "percolation of words". We give a positive answer to their Open Problem 2: almost surely, all…
We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we…
A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph…
We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. This is a special case of a conjecture due to O.…
Let H_n be the hypercube {0,1}^n, and let H_{n,p} denote the same graph with Bernoulli bond percolation with parameter p=n^-\alpha. It is shown that at \alpha=1/2 there is a phase transition for the metric distortion between H_n and…
We consider bond and site Bernoulli Percolation in both the oriented and the non-oriented cases on $\mathbb{Z}^d$ and obtain rigorous upper bounds for the critical points in those models for every dimension $d \geq 3$.