Related papers: The initial set in the frog model is irrelevant

Numerical continuation is used to compute solution branches in a two-component reaction-diffusion model of Leslie--Gower type. %in the vicinity of a Turing-Hopf interaction. Two regimes are studied in detail. In the first, the homogeneous…

We study a coupled driven system in which two species of particles are advected by a fluctuating potential energy landscape. While the particles follow the potential gradient, each species affects the local shape of the landscape in…

Dynamics of two particles with short range repulsive or attractive interaction is studied numerically in the Harper model. It is shown that interaction leads to appearance of localized states and pure-point spectrum component in the case…

We extend a non local and non covariant version of the Thirring model in order to describe a many-body system with spin-flipping interactions By introducing a model with two fermion species we are able to avoid the use of non abelian…

We reinvestigate the validity of mapping the problem of two onsite interacting particles in a random potential onto an effective random matrix model. To this end we first study numerically how the non-interacting basis is coupled by the…

We construct a two-class asymmetric interacting particle system with $U_q(so_6)$ or $U_q(so_8)$ symmetry, in which up to two particles may occupy a site if the two particles have different class. The particles exhibit a drift, but there is…

Using a simple probabilistic model, we illustrate that a small part of a strongly correlated many-body classical system can show a paradoxical behavior, namely asymptotic stochastic independence. We consider a triangular array such that…

One-photon and Raman type interactions between two-level atoms and narrow-band light are considered. We give some exactly solvable models of these processes when only one-photon Fock states are involved in the evolution. Possible…

In this work we consider a size-structured cannibalism model with the model ingredients (fertility, growth, and mortality rate) depending on size (ranging over an infinite domain) and on a general function of the standing population…

There are two types $i=1,2$ of particles on the line $R$, with $N_{i}$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_{i}$. Moreover, any particle of type $i=1,2$ jumps to any particle of type $j=1,2$ with…

In this paper we observe the frog model, an infinite system of interacting random walks, on Z with an asymmetric underlying random walk. Under the assumption of transience with a fixed frog distribution, we construct an explicit formula for…

We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…

We present a model for the evolution of networks of occupied sites on undirected regular graphs. At every iteration step in a parallel update I randomly chosen empty sites are occupied and occupied sites having degree outside of a given…

We consider a non relativistic quantum system consisting of $K$ heavy and $N$ light particles in dimension three, where each heavy particle interacts with the light ones via a two-body potential $\alpha V$. No interaction is assumed among…

We theoretically investigate the full time evolution of a nonequilibrium double quantum dot structure from initial conditions corresponding to different product states (no entanglement between dot and lead) to a nonequilibrium steady state.…

We consider the asymptotic behavior of the (one dimensional) two-species annihilation reaction A + B --> 0, where both species have a uniform drift in the same direction and like species have a hard core exclusion. Extensive numerical…

We study the asymptotic behavior of the maximum degree in the preferential attachment model with a choice-based edge-step. We add vertex type to the model and prove, among others types of behavior, the effect of condensation on multiple…

We consider an evolution of two elementary quantum particles and ask the question: under what conditions such a system behaves as a single object? It is obvious that if the attraction between the particles is stronger than any other force…

This paper provides a survey of known results and open problems for the two-type Richardson model, which is a stochastic model for competition on $\mathbb{Z}^d$. In its simplest formulation, the Richardson model describes the evolution of a…

This paper introduces a new family of models of intensional Martin-L\"of type theory. We use constructive ordered algebra in toposes. Identity types in the models are given by a notion of Moore path. By considering a particular gros topos,…