Related papers: Particle systems with singular interaction through…

We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution…

We describe the macroscopic behaviour of a particle system with long-range interactions. We describe conditions on the interaction strength in dependency of the distance of the particles, such that the scaling limit of the particle system…

We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…

We consider a family of McKean--Vlasov equations arising as the large particle limit of a system of interacting particles on the positive half-line with common noise and feedback. Such systems are motivated by structural models for systemic…

This paper studies the boundary behaviour at mechanical equilibrium at the ends of a finite interval of a class of systems of interacting particles with monotone decreasing repulsive force. Our setting covers pile-ups of dislocations,…

In this paper, we consider particle systems with interaction and Brownian motion. We prove that when the initial data is from the sampling of Chorin's method, i.e., the initial vertices are on lattice points $hi\in \mathbb{R}^d$ with mass…

In our model, private actors with interbank cash flows similar to, but nore general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a certain interest rate, controlled by the central bank, and invest in risky assets.…

We perform finite element simulations to study the impact of defect-defect interactions on the pressure-induced buckling of thin, elastic, spherical shells containing two dimpled imperfections. Throughout, we quantify the critical buckling…

A macroscopic hydrodynamic system that couples a particle and a wave has recently renewed interest in the question as to what extent a classical system may reproduce quantum phenomena. Here we investigate single-particle diffraction with a…

We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…

We study a McKean--Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier they cause the other particles to jump in the direction of the barrier and this feedback mechanism…

Interacting particle systems play a key role in science and engineering. Access to the governing particle interaction law is fundamental for a complete understanding of such systems. However, the inherent system complexity keeps the…

Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…

The classical reduced-form and filtration expansion framework in credit risk is extended to the case of multiple, non-ordered defaults, assuming that conditional densities of the default times exist. Intensities and pricing formulas are…

This paper proves an instability theorem for dynamical systems. As one adds interactions between subystems in a complex system, structured or random, a threshold of connectivity is reached beyond which the overall dynamics inevitably goes…

This study investigates the functioning of modern payment systems through the lens of banks' maturity mismatch practices, and it examines the effects of banks' refusal to roll over short-term interbank liabilities on financial stability.…

We introduce a framework to prove propagation of chaos for interacting particle systems with singular, density-dependent interactions, a classical challenge in mean-field theory. Our approach is to define the dynamics implicitly via a…

The question of how to stabilize financial systems has attracted considerable attention since the global financial crisis of 2007-2009. Recently, Beale et al. ("Individual versus systemic risk and the regulator's dilemma", Proc Natl Acad…

We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an…

We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…