Related papers: Coexistence probability in the last passage percol…
This paper presents three results on dependent site percolation on the square lattice. First, there exists no positively associated probability measure on {0,1}^{Z^2} with the following properties: a) a single infinite 0cluster exists…
We introduce new probabilistic arguments to derive optimal-order central moment bounds in planar directed last-passage percolation. Our technique is based on couplings with the increment-stationary variants of the model, and is presented in…
We consider first-passage percolation on $\mathbb Z^2$ with independent and identically distributed weights whose common distribution is absolutely continuous with a finite exponential moment. Under the assumption that the limit shape has…
We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair…
Recent studies aimed at investigating artificial analogs of bacterial colonies have shown that low-density suspensions of self-propelled particles confined in two dimensions can assemble into finite aggregates that merge and split, but have…
Critical phenomena of a second-order percolation transition are known to be independent of cluster merging or pruning process. However, those of a hybrid percolation transition (HPT), mixed properties of both first-order and second-order…
The equilibrium states associated with the local majority-rule are divided into three classes, the states of system-wide coordination, the trapped states, and the states of period-2. The effect of clustering coefficient on the occurrence…
In this note, we study the model of directed last passage percolation on $\mathbb{Z}^2$, with i.i.d. exponential weight. We consider the maximum paths from vertices $\left(0,\lfloor k^{2/3} \rfloor\right)$ and $(\lfloor k^{2/3} \rfloor,0)$…
Zhang found a simple, elegant argument deducing the non-existence of an infinite open cluster in certain lattice percolation models (for example, p=1/2 bond percolation on the square lattice) from general results on the uniqueness of an…
Triangles are abundant in real-world networks but rare in standard null models for sparse graphs. Existing explanations typically rely on explicit triadic closure mechanisms or geometry-based connection rules. We propose an alternative…
We consider a last passage percolation model in dimension $1+1$ with potential given by the product of a spatial i.i.d. potential with symmetric bounded distribution and an independent i.i.d. in time sequence of signs. We assume that the…
We consider a variation of the Hastings-Levitov model HL(0) for random growth in which the growing cluster consists of two competing regions. We allow the size of successive particles to depend both on the region in which the particle is…
We give a quantitative analysis of clustering in a stochastic model of one-dimensional gas. At time zero, the gas consists of $n$ identical particles that are randomly distributed on the real line and have zero initial speeds. Particles…
Motivated by aggregation phenomena in gliding bacteria, we study collective motion in a twodimensional model of active, self-propelled rods interacting through volume exclusion. In simulations with individual particles, we find that…
We study here one-dimensional model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. Isolated…
In this paper we prove a duality relation between coalescence times and exit points in last-passage percolation models with exponential weights. As a consequence, we get lower bounds for coalescence times with scaling exponent 3/2, and we…
Neuhauser [Probab. Theory Related Fields 91 (1992) 467--506] considered the two-type contact process and showed that on $\mathbb{Z}^2$ coexistence is not possible if the death rates are equal and the particles use the same dispersal…
We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…
Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…
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…