Related papers: Fredrickson Andersen Model and Noisy Majority Vote…
Facilitated spin models were introduced some decades ago to mimic systems characterized by a glass transition. Recent developments have shown that a class of facilitated spin models is also able to reproduce characteristic signatures of the…
We analyze dynamical systems subjected to an additive noise and their deterministic limit. In this work, we will introduce a notion by which a stochastic system has something like a Markov partition for deterministic systems. For a chosen…
We study the static and dynamic structure of thermally fluctuating elastic thin sheets by investigating the overdamped dynamic F\"oppl-von K\'arm\'an equation, in which the F\"oppl-von K\'arm\'an equation from elasticity theory is driven by…
The Fredrickson-Andersen 2-spin facilitated model on $\mathbb{Z}^d$ (FA-2f) is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring dynamical facilitation, an important mechanism in condensed matter physics.…
Online social networks are ubiquitous parts of modern societies and the discussions that take place in these networks impact people's opinions on diverse topics, such as politics or vaccination. One of the most popular models to formally…
We consider a nonlocal evolution equation representing the continuum limit of a large ensemble of interacting particles on graphs forced by noise. The two principle ingredients of the continuum model are a nonlocal term and Q-Wiener process…
We study condensation in several particle systems related to the inclusion process. For an asymmetric one-dimensional version with closed boundary conditions and drift to the right, we show that all but a finite number of particles condense…
We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from…
The behavior of non-spherical particles in a shear-flow is of significant practical and theoretical interest. These systems have been the object of numerous investigations since the pioneering work of Jeffery a century ago. His eponymous…
An aggregated model is proposed, of which the partial-sum process scales to the Karlin stable processes recently investigated in the literature. The limit extremes of the proposed model, when having regularly-varying tails, are…
This article starts by introducing a new theoretical framework to model spatial systems which is obtained from the framework of interacting particle systems by replacing the traditional graphical structure that defines the network of…
We study a low temperature anisotropic anti-ferromagnetic 2D Ising model through the guise of a certain dimer model. This model has a bijection with a one-dimensional particle system equipped with creation and annihilation. In the…
We analyze large deviations of the time-averaged activity in the one dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large…
We consider the two-opinion voter model on a regular random graph with n vertices and degree $d \geq 3$. It is known that consensus is reached on time scale n and that on this time scale the volume of the set of vertices with one opinion…
The J\'{a}nossy density for a determinantal point process is the probability density that an interval $I$ contains exactly $p$ points except for those at $k$ designated loci. The J\'{a}nossy density associated with an integrable kernel…
This paper introduces new empirical process tools for analyzing a broad class of statistical learning models under heavy-tailed noise and complex function classes. Our primary contribution is the derivation of two Dudley-type maximal…
In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…
We consider the fluctuations in the number of particles in a box of size L^d in Z^d, d>=1, in the (infinite volume) translation invariant stationary states of the facilitated exclusion process, also called the conserved lattice gas model.…
This paper establishes the global well-posedness of the nonlinear Fokker-Planck equation for a noisy version of the Hegselmann-Krause model. The equation captures the mean-field behavior of a classic multiagent system for opinion dynamics.…
In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…