Related papers: Particle systems with singular interaction through…
In this paper we propose a new nonparametric approach to interacting failing systems (FS), that is systems whose probability of failure is not negligible in a fixed time horizon, a typical example being firms and financial bonds. The main…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
We study the limiting behavior of an interacting particle system evolving on the lattice $Z^{d}$ for $d\ge 3$. The model is known as the contact process with rapid stirring. The process starts with a single particle at the origin. Each…
We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
We consider a system of charged particles moving on the real line driven by electrostatic interactions. Since we consider charges of both signs, collisions might occur in finite time. Upon collision, some of the colliding particles are…
In this short survey we compare aspects of two different approaches for scaling limits of interacting particle systems, the hydrodynamic limit and the high density limit. We present some examples, comments and open problems on each approach…
In this work we study a kinetic model of active particles with delayed dynamics, and its limit when the number of particles goes to infinity. This limit turns out to be related to delayed differential equations with random initial…
In this article, we study the large-population limit of interacting particle systems posed on weighted random graphs. In that aim, we introduce a general framework for the construction of weighted random graphs, generalizing the concept of…
We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction…
We introduce a heterogeneous formulation of a contagious McKean-Vlasov system, whose inherent heterogeneity comes from asymmetric interactions with a natural and highly tractable structure. It is shown that this formulation characterises…
We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the…
The 2008 financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
We study an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. If a particle is the minimal-label particle at its site when it…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
In this work, we investigate the dynamics of interacting particle systems subjected to repulsive forces, such as lattices of magnetized particles. To this end, we first develop a general model capable of capturing the complete dynamical…