相关论文: Diffractive point sets with entropy

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…

Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…

The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…

Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker map, as well as spatially periodic systems of interacting particles, have non-equilibrium stationary states with fractal properties when put in contact with…

This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides of this theory as well as diffraction and the connection…

Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…

The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…

This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…

Grid entropy is a deterministic quantity inherent to lattice models which captures the entropy of empirical measures along paths that converge weakly to a given target measure. In this paper, we study the limiting behaviour of empirical…

Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…

The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

We study point sets arising from cut-and-project constructions. An important class is weak model sets, which include squarefree numbers and visible lattice points. For such model sets, we give a non-trivial upper bound on their pattern…

We define the notion of localizable property for a dynamical system. Then we survey three properties of complexity and relate how they are known to be typical among differentiable dynamical systems. These notions are the fast growth of the…

We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a…

We study diffusive lattice gases with local injection of particles, namely we assume that whenever the origin becomes empty, a new particle is immediately injected into the origin. We consider two lattice gases: a symmetric simple exclusion…

Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical…

Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in…

We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…

Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of translations of a lattice. This leads us to the concept of…