相关论文: First passage percolation and a model for competin…

We revisit the problem of local persistence in directed percolation, reporting improved estimates of the persistence exponent in 1+1 dimensions, discovering strong corrections to scaling in higher dimensions, and investigating the mean…

Noise and spatial degrees of freedom characterize most ecosystems. Some aspects of their influence on the coevolution of populations with cyclic interspecies competition have been demonstrated in recent experiments [e.g. B. Kerr et al.,…

The main contribution of this paper is the development of a novel approach to multi-scale analysis that we believe can be used to analyse processes with non-equilibrium dynamics. Our approach will be referred to as \emph{multi-scale…

Suppose that $nk$ points in general position in the plane are colored red and blue, with at least $n$ points of each color. We show that then there exist $n$ pairwise disjoint convex sets, each of them containing $k$ of the points, and each…

In the first part of this paper we propose a new theoretical model of city growth based on percolation. The second half oh the paper is devoted to a concrete application of the model, namely to the city of Montargis. It appears that the…

Camouflage in nature seems to arise from competition between predator and prey. To survive, predators must find prey, and prey must avoid being found. This work simulates an abstract model of that adversarial relationship. It looks at…

We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…

The adoption of agroecological practices will be crucial to address the challenges of climate change and biodiversity loss. Such practices favor the cultivation of plants in complex mixtures with layouts differing from the monoculture…

The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…

A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on…

A spatial co-location pattern represents a subset of spatial features whose instances are prevalently located together in a geographic space. Although many algorithms of mining spatial co-location pattern have been proposed, there are still…

For rotationally invariant first passage percolation (FPP) on the plane, we use a multi-scale argument to prove stretched exponential concentration of the first passage times at the scale of the standard deviation. Our results are proved…

The study of first passage percolation (FPP) for the random interlacements model has been initiated in arXiv:2112.12096, where it is shown that on $\mathbb{Z}^d$, $d\geq 3$, the FPP distance is comparable to the graph distance with high…

We introduce a continuum percolation model defined on the points of a d-dimensional homogeneous Poisson process. Each Poisson point is connected to all points within its connection range, which depends on the distances to the other Poisson…

We employ simulations of model proteins to study folding on rugged energy landscapes. We construct ``first-passage'' networks as the system transitions from unfolded to native states. The nodes and bonds in these networks correspond to…

We propose a metric space of coalescing pairs of paths on which we are able to prove (more or less) directly convergence of objects such as the persistence probability in the (one dimensional, nearest neighbor, symmetric) voter model or the…

We establish the scaling limit of the geodesics to the root for the first passage percolation distance on random planar maps. We first describe the scaling limit of the number of faces along the geodesics. This result enables us to compare…

In this paper, we consider coloring of graphs under the assumption that some vertices are already colored. Let $G$ be an $r$-colorable graph and let $P\subset V(G)$. Albertson [J.\ Combin.\ Theory Ser. B \textbf{73} (1998), 189--194] has…

For some m \ge 4, let us color each column of the integer lattice L = Z^2 independently and uniformly into one of m colors. We do the same for the rows, independently from the columns. A point of L will be called blocked if its row and…

We propose a general population dynamics model for two seagrass species growing and interacting in two spatial dimensions. The model includes spatial terms accounting for the clonal growth characteristics of seagrasses, and coupling between…