Related papers: Quasistationary Distribution for the Invasion Mode…
We consider the discrete-time voter model on complete bipartite graphs and study the quasi-stationary distribution (QSD) for the model as the size of one of the partitions tends to infinity while the other partition remains fixed. We show…
We present a mathematical description of the voter model dynamics on heterogeneous networks. When the average degree of the graph is $\mu \leq 2$ the system reaches complete order exponentially fast. For $\mu >2$, a finite system falls,…
We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the…
We solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with <k^1/2>. In contrast, earlier results studying the problem in graphs with…
In this paper we study the asymptotic behavior of the normalized weighted empirical occupation measures of a diffusion process on a compact manifold which is killed at a smooth rate and then regenerated at a random location, distributed…
In the present work we characterize the existence of quasistationary distributions for diffusions on $(0,\infty)$ allowing singular behavior at $0$ and $\infty$. If absorption at 0 is certain, we show that there exists a quasistationary…
In the setting of stochastic dynamical systems that eventually go extinct, the quasi-stationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time…
We study statistical properties of the energy spectra of two-dimensional quasiperiodic tight-binding models. The multifractal nature of the eigenstates of these models is corroborated by the scaling of the participation numbers with the…
A model algorithm is proposed to study subsequent partitions of complex networks describing social structures. The partitions are supposed to appear as actions of rivaling leaders corresponding to nodes with large degrees. The condition of…
We study the long-time behavior of stochastic models with an absorbing state, conditioned on survival. For a large class of processes, in which saturation prevents unlimited growth, statistical properties of the surviving sample attain…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We…
We study a stochastic system of $N$ interacting particles which models bimolecular chemical reaction-diffusion. In this model, each particle $i$ carries two attributes: the spatial location $X_t^i\in \mathbb{T}^d$, and the type $\Xi_t^i\in…
This article studies the quasi-stationary behaviour of multidimensional birth and death processes, modeling the interaction between several species, absorbed when one of the coordinates hits 0. We study models where the absorption rate is…
We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation measure when it reaches the boundary. We show that its…
A model of quasistationary states is constructed for the one-dimensional edge states propagating along the edge of a two-dimensional topological insulator based on HgTe/CdTe quantum well in the presence of magnetic barriers with finite…
We consider a totally asymmetric exclusion process on the positive half-line. When particles enter in the system according to a Poisson source, Liggett has computed all the limit distributions when the initial distribution has an asymptotic…
Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…
Along the line of thoughts of Berry and Robnik{\cite{Ber}}, the limiting gap distribution function of classically integrable quantum systems is derived in the limit of infinitely many independent components. The limiting gap distribution…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…