Related papers: Diffractive point sets with entropy
We consider a tracer particle on a lattice in the presence of immobile obstacles. Starting from equilibrium, a force pulling on the particle is switched on, driving the system to a new stationary state. We solve for the complete transient…
We propose two distributed set-based observers using strip-based and set-propagation approaches for linear discrete-time dynamical systems with bounded modeling and measurement uncertainties. Both algorithms utilize a set-based diffusion…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
A simple lattice gas model in one dimension is constructed in which each site can be occupied by at most one particle of any one of $D$ species. Particles interact with a randomly drawn nearest neighbor interaction. This model is capable of…
The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared.…
Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this…
The dynamical rules in auxiliary stochastic process that generates the biased ensemble of rare events are non-local. For the systems with one type of particle, it is shown that there are special cases for which the generators of effective…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including…
Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on local-in-time existence results for general systems with normally elliptic diffusion operators, due to Amann, and global-in-time existence theorems…
A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
We analyze the emergence of diffractive focusing in the transition from discrete to continuous space-time variables. Three types of dynamical equations are studied in a top-to-bottom approach, starting with the most general system. First we…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…
Within the setting of rare event modelling, the method of level sets allows us to define an equivalence relation over rare events with distinct rates of entropy production. This method allows us to clarify the relation between the empirical…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
A two-dimensional lattice gas model is proposed. The ground state of this model with a fixed density is neither periodic nor quasi-periodic. It also depends on system size in an irregular manner. On the other hand, it is ordered in the…
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…
We consider an interacting particle system on the one dimensional lattice $\bf Z$ modeling combustion. The process depends on two integer parameters $2\le a<M<\infty$. Particles move independently as continuous time simple symmetric random…