Related papers: Phase transitions for interacting particle systems…
The goal of this paper is to approximate several kinds of {\it Mckean-Vlasov SDEs} with {\it irregular coefficients} via weakly interacting particle systems. More precisely, propagation of chaos and convergence rate of Euler-Maruyama scheme…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
In this paper, we use rigorous numerics to compute several global smooth branches of steady states for a system of three reaction-diffusion PDEs introduced by Iida et al. [J. Math. Biol., {\bf 53}, 617--641 (2006)] to study the effect of…
In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of…
Recent advances in generating well controlled dense arrangements of individual atoms in free space have generated interest in understanding how the extended nature of these systems influences superradiance phenomena. Here, we provide an…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…
Recently, the percolation transition has been characterized on interacting networks both in presence of interdependent and antagonistic interactions. Here we characterize the phase diagram of the percolation transition in two Poisson…
This paper establishes an indirect approximation theorem for the most probable transition pathway of a stochastic interacting particle system in the mean-field framework. This paper studied the problem of indirect approximation of the most…
Ultra-cold atomic systems are among the most promising platforms that have the potential to shed light on the complex behavior of many-body quantum systems. One prominent example is the case of a dense ensemble illuminated by a strong…
Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker map, as well as spatially periodic systems of interacting particles, have non-equilibrium stationary states with fractal properties when put in contact with…
Deviations from the perfect atomic arrangements in crystals play an important role in affecting their properties. Similarly, diffusion of such deviations is behind many microstructural changes in solids. However, observation of point defect…
We prove limit theorems for systems of interacting diffusions on sparse graphs. For example, we deduce a hydrodynamic limit and the propagation of chaos property for the stochastic Kuramoto model with interactions determined by…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
We analyze the existence and the size of the giant component in the stationary state of a Markovian model for bipartite multigraphs, in which the movement of the edge ends on one set of vertices of the bipartite graph is a zero-range…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
The contact process is a stochastic process which exhibits a continuous, absorbing-state phase transition in the Directed Percolation (DP) universality class. In this work, we consider a contact process with a bias in conjunction with an…
We consider a system of $N$ disordered mean-field interacting diffusions within spatial constraints: each particle $\theta_i$ is attached to one site $x_i$ of a periodic lattice and the interaction between particles $\theta_i$ and…
Graphene and its multilayers have attracted considerable interest owing to the fourfold spin and valley degeneracy of their charge carriers, which enables the formation of a rich variety of broken-symmetry states and raises the prospect of…