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The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
We present a unified framework, with quantitative estimates, for deterministic interacting particle systems whose pairwise interactions may depend on heterogeneous labels. Heterogeneity is kept at every level by adding a frozen label…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
We address the problem of estimating the drift parameter in a system of $N$ interacting particles driven by additive fractional Brownian motion of Hurst index \( H \geq 1/2 \). Considering continuous observation of the interacting particles…
We study causal effect estimation from observational data under interference. The interference pattern is captured by an observed network. We adopt the chain graph framework of Tchetgen Tchetgen et. al. (2021), which allows (i) interaction…
We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…
We express the partition function for an equilibrium system of interacting particles in the canonical ensemble as a functional integration over the particles' density field. We outline a method to evaluate the partition function by…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
Many processes in biology, chemistry, physics, medicine, and engineering are modeled by a system of differential equations. Such a system is usually characterized via unknown parameters and estimating their 'true' value is thus required. In…
This paper investigates the limit behavior of Markov Decision Processes (MDPs) made of independent particles evolving in a common environment, when the number of particles goes to infinity. In the finite horizon case or with a discounted…
Particle- and agent-based systems are a ubiquitous modeling tool in many disciplines. We consider the fundamental problem of inferring interaction kernels from observations of agent-based dynamical systems given observations of…
This paper studies the Gibbs measure of an interacting particle system with a general interaction kernel at various temperature regimes. We are particularly interested in fine features of the convergence to the mean-field density as the…
We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…
Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy…
A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with $S = \tfrac12$ and external field. For large…
This paper investigates the use of transformers to approximate the mean-field dynamics of interacting particle systems exhibiting collective behavior. Such systems are fundamental in modeling phenomena across physics, biology, and…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
In this paper, we study a model for opinion dynamics where the influence weights of agents evolve in time via an equation which is coupled with the opinions' evolution. We explore the natural question of the large population limit with two…
We construct an exactly solvable circuit of interacting memristors and study its dynamics and fixed points. This simple circuit model interpolates between decoupled circuits of isolated memristors, and memristors in series, for which exact…
Estimation of stochastic processes evolving in a random environment is of crucial importance for example to predict aircraft trajectories evolving in an unknown atmosphere. For fixed parameter, interacting particle systems are a convenient…