Related papers: Hydrodynamic Limits of non-Markovian Interacting P…
We study the hydrodynamic limit for a periodic $1$-dimensional exclusion process with a dynamical constraint, which prevents a particle at site $x$ from jumping to site $x\pm1$ unless site $x\mp1$ is occupied. This process with degenerate…
We study a class of graphon particle systems with time-varying random coefficients. In a graphon particle system, the interactions among particles are characterized by the coupled mean field terms through an underlying graphon and the…
The starting point of our analysis is a class of one-dimensional interacting particle systems with two species. The particles are confined to an interval and exert a nonlocal, repelling force on each other, resulting in a nontrivial…
We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the…
Markovian evolving graphs are dynamic-graph models where the links among a fixed set of nodes change during time according to an arbitrary Markovian rule. They are extremely general and they can well describe important dynamic-network…
This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate…
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all the particles. If this local time drift is too strong, such…
We consider a system of $N$ interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position.…
We use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend…
Interacting particle systems provide a fundamental framework for modeling collective behavior in biological, social, and physical systems. In many applications, stochastic perturbations are essential for capturing environmental variability…
We study a model for flocking given by a $n$-particle system under which each particle jumps forward by a random amount, independently sampled from a given distribution $\theta$, with rate given by a non-increasing function $w$ of its…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In…
Generic interacting many-body quantum systems are believed to behave as classical fluids on long time and length scales. Due to rapid progress in growing exceptionally pure crystals, we are now able to experimentally observe this collective…
We derive a quantitative version of the hydrodynamic limit for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the $L^2$-speed of convergence of the empirical density of states in a…
Particle-particle interactions are of paramount importance in every multi-body system as they determine the collective behaviour and coupling strength. Many well-known interactions like electro-static, van der Waals or screened Coulomb,…
Although the dynamics of colloids in the vicinity of a solid interface has been widely characterized in the past, experimental studies of Brownian diffusion close to an air-water interface are rare and limited to particle-interface gap…
We consider a model of lattice gas dynamics in the d-dimensional cubic lattice in the presence of disorder. If the particle interaction is only mutual exclusion and if the disorder field is given by i.i.d. bounded random variables, we prove…
Recent microfluidic experiments revealed that large particles advected in a fluidic loop display long-range hydrodynamic interactions. However, the consequences of such couplings on the traffic dynamics in more complex networks remain…
Hydrodynamics provides a successful framework to effectively describe the dynamics of complex many-body systems ranging from subnuclear to cosmological scales by introducing macroscopic quantities such as particle densities and fluid…