相关论文: Competition between growths governed by Bernoulli …
We investigate locality of the supercritical regime for Bernoulli percolation on transitive graphs with polynomial growth, by which we mean the following. Take a transitive graph of polynomial growth $\mathscr{G}$ satisfying…
The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms through which extinction of infection propagation comes about. We here report on a…
We introduce a new model of competition on growing networks. This extends the preferential attachment model, with the key property that node choices evolve simultaneously with the network. When a new node joins the network, it chooses…
The paper is concerned with different types of dispersal chosen by competing species. We introduce a model with the diffusion-type term $\nabla \cdot \left[ a \nabla \left( u/P \right) \right]$ which includes some previously studied systems…
The possibility of coexistence of two competing populations is a classical question which dates back to the earliest `predator-prey' models. In this paper we study this question in the context of a model for the spread of a virus infection…
We study a competitive stochastic growth model called chase-escape in which red particles spread to adjacent uncolored sites and blue only to adjacent red sites. Red particles are killed when blue occupies the same site. If blue has rate-1…
We consider the random cluster model with parameter $q<1$, for which the FKG inequalities are not valid. On the square lattice, stochastic comparison with Bernoulli percolation implies that the model is subcritical (respectively…
Probabilities of measurement outcomes of two-particle entangled states give a physically transparent interpretation of the concurrence and of the I-concurrence as entanglement measures. The (I)-concurrence can thus be measured…
We consider independent and $m$-dependent two-dimensional oriented site percolation with open-site density close to one started from Bernoulli product measures. We show that the probability of an occupied interval in the former process…
We show that a superposition of an $\varepsilon$-Bernoulli bond percolation and any everywhere percolating subgraph of $\mathbb Z^d$, $d\ge 2$, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli…
We consider the Bernoulli percolation model in a finite box and we introduce an automatic control of the percolation probability, which is a function of the percolation configuration. For a suitable choice of this automatic control, the…
There exists a Lipschitz embedding of a d-dimensional comb graph (consisting of infinitely many parallel copies of Z^{d-1} joined by a perpendicular copy) into the open set of site percolation on Z^d, whenever the parameter p is close…
A simple but powerful network model with $n$ nodes and $m$ partly overlapping layers is generated as an overlay of independent random graphs $G_1,\dots,G_m$ with variable sizes and densities. The model is parameterised by a joint…
This paper investigates the coexistence of two competing species on random geometric graphs (RGGs) in continuous time. The species grow by occupying vacant sites according to Richardson's model, while simultaneously competing for occupied…
Entanglement concurrence is an important bipartite entanglement measure that has found wide applications in quantum technologies. In this work, inspired by unified entropy, we introduce a two-parameter family of entanglement measures,…
Diseases spread through host populations over the networks of contacts between individuals, and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond…
We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not…
In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of…
Competing interactions stabilize exotic mesoscopic structures, yet the microscopic mechanisms by which they influence non-equilibrium processes leading to disordered states remain largely unexplored, despite their critical role in…
We propose two models of the evolution of a pair of competing populations. Both are lattice based. The first is a compromise between fully spatial models, which do not appear amenable to analytic results, and interacting particle system…