Related papers: Coexistence probability in the last passage percol…
We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and…
We consider a class of interacting particle systems with values in $[0,\8)^{\zd}$, of which the binary contact path process is an example. For $d \ge 3$ and under a certain square integrability condition on the total number of the…
In this paper we consider Bernoulli percolation on an infinite connected bounded degrees graph $G$. Assuming the uniqueness of the infinite open cluster and a quasi-multiplicativity of crossing probabilities, we prove the existence of…
We study a competition model on $\mathbb{Z}^d$ where the two infections are driven by supercritical Bernoulli percolations with distinct parameters $p$ and $q$. We prove that, for any $q$, there exist at most countably many values of…
Compartmentalization of self-replicating molecules (templates) in protocells is a necessary step towards the evolution of modern cells. However, coexistence between distinct template types inside a protocell can be achieved only if there is…
We use N-body simulations to survey the response of embedded star clusters to the dispersal of their parent molecular cloud. The final stages of the clusters can be divided into three classes: the cluster (i) is destroyed, (ii) has a loose…
We introduce a notion of capacity for high dimensional critical percolation by showing that for any finite set $A$, the suitably rescaled probability that the cluster of $z$ intersects $A$ converges as $\|z\|\to\infty$. This can be viewed…
There are two modes by which clusters of aggregating particles can coalesce: The clusters can merge either (i) by the Ostwald ripening process in which particles diffuse from one cluster to the other whilst the cluster centres remain…
The probabilities of clusters spanning a hypercube of dimensions two to seven along one axis of a percolation system under criticality were investigated numerically. We used a modified Hoshen--Kopelman algorithm combined with Grassberger's…
We study site percolation on lattices confined to a semi-infinite strip. For triangular and square lattices we find that the probability that a cluster touches the three sides of such a system at the percolation threshold has the continuous…
In this paper, we study a distribution of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations…
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…
In the polluted bootstrap percolation model, vertices of the cubic lattice $\mathbb{Z}^3$ are independently declared initially occupied with probability $p$ or closed with probability $q$. Under the standard (respectively, modified)…
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…
In last passage percolation models, the energy of a path is maximized over all directed paths with given endpoints in a random environment, and the maximizing paths are called geodesics. The geodesics and their energy can be scaled so that…
We study a model of aggregation and fragmentation of clusters of particles on an open segment of a single-lane road. The particles and clusters obey the stochastic discrete-time discrete-space kinetics of the Totally Asymmetric Simple…
We investigate a model of interacting clusters which compete for growth. For a finite assembly of coupled clusters, the largest one always wins, so that all but this one die out in a finite time. This scenario of `survival of the biggest'…
We study the dynamics and clustering of dust particles with inertia in shock-dominated compressible turbulence using the two-dimensional, stochastically forced Burgers equation. At small Stokes numbers, shock trapping leads to extreme…
We show that for all p>p_c(\Z^d) percolation parameters, the probability that the cluster of the origin is finite but has at least t vertices at distance one from the infinite cluster is exponentially small in t. We use this to give a short…
Some examples of translation invariant site percolation processes on the $\Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the probability that a site is open given…