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We prove that every probabilistic cellular automaton with strictly positive transition probabilities that admits a stationary Bernoulli measure is exponentially ergodic. Moreover, the mixing time of any finite region in such a system is…
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…
On a fine grained scale the Gibbs entropy of an isolated system remains constant throughout its dynamical evolution. This is a consequence of Liouville's theorem for Hamiltonian systems and appears to contradict the second law of…
We study a stochastic particle system which models the time evolution of the ranking of books by online bookstores (e.g., Amazon). In this system, particles are lined in a queue. Each particle jumps at random jump times to the top of the…
We study a stochastic $N$-particle system representing economic agents in a population randomly exchanging their money, which is associated to a class of one-dimensional kinetic equations modelling the evolution of the distribution of…
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…
Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…
We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…
The random batch Ewald (RBE) is an efficient and accurate method for molecular dynamics (MD) simulations of physical systems at the nano-/micro- scale. The method shows great potential to solve the computational bottleneck of long-range…
The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields…
In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian Mean Field model and show that the life-time of…
We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert particle increases due to the influence of an external…
We present here for the first time a unifying perspective for the lack of equipartition in non-linear ordered systems and the low temperature phase-space fragmentation in disordered systems. We demonstrate that they are just two…
We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic…
Coulomb interaction, following an inverse-square force-law, quantifies the amount of force between two stationary and electrically charged particles. The long-range nature of Coulomb interactions poses a major challenge to molecular…
Methods to extract information from the tracking of mobile objects/particles have broad interest in biological and physical sciences. Techniques based on simple criteria of proximity in time-consecutive snapshots are useful to identify the…
This article addresses the problem of efficient Bayesian inference in dynamic systems using particle methods and makes a number of contributions. First, we develop a correlated pseudo-marginal (CPM) approach for Bayesian inference in state…
The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary…
We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…