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A concept of emergence was recently introduced in the paper [Berger] in order to quantify the richness of possible statistical behaviors of orbits of a given dynamical system. In this paper, we develop this concept and provide several new…
Multiple image gravitational lens systems, and especially quads are invaluable in determining the amount and distribution of mass in galaxies. This is usually done by mass modeling using parametric or free-form methods. An alternative way…
The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…
Scientists need to compare the support for models based on observed phenomena. The main goal of the evidential paradigm is to quantify the strength of evidence in the data for a reference model relative to an alternative model. This is done…
The statistical inference of stochastic block models as emerged as a mathematicaly principled method for identifying communities inside networks. Its objective is to find the node partition and the block-to-block adjacency matrix of maximum…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
In this review, we present econometric and statistical methods for analyzing randomized experiments. For basic experiments we stress randomization-based inference as opposed to sampling-based inference. In randomization-based inference,…
The aim of this paper is to study the asymptotic properties of a class of kernel conditional mode estimates whenever functional stationary ergodic data are considered. To be more precise on the matter, in the ergodic data setting, we…
Suppose that we are interested in the comparison of two independent categorical variables. Suppose also that the population is divided into subpopulations or groups. Notice that the distribution of the target variable may vary across…
We study the thermalization properties of a fully nonlinear lattice model originally derived from the two-dimensional cubic defocusing nonlinear Schr\"odinger equation (NLS) using analytical and numerical methods. Our analysis reveals both…
We consider the ergodicity and consensus problem for a discrete-time linear dynamic model driven by random stochastic matrices, which is equivalent to studying these concepts for the product of such matrices. Our focus is on the model where…
Spectral densities encode the relevant information characterising the system-environment interaction in an open-quantum system problem. Such information is key to determining the system's dynamics. In this work, we leverage the potential of…
A partially non-ergodic ground-motion prediction equation is estimated for Europe and the Middle East. Therefore, a hierarchical model is presented that accounts for regional differences. For this purpose, the scaling of ground-motion…
A method for inverting the statistical star counts equation, including proper motions, is presented; in order to break the degeneracy in that equation it uses the supplementary constraints required by dynamical consistency. The inversion…
An open question in the field of non-equilibrium statistical physics is whether there exists a unique way through which non-equilibrium systems equilibrate irrespective of how far they are away from equilibrium. To answer this question we…
Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications,…
We discuss ergodicity breaking in frustrated disordered systems with no apparent broken symmetry of the Hamiltonian and present a way how to amend it in the low-temperature phase. We demonstrate this phenomenon on mean-field models of spin…
The definition of thermodynamic entropy is dependent on one's assignment of physical microstates to observed macrostates. As a result, low entropy in the distant past could be equivalently explained by selection of a particular observer. In…
In this paper, we introduce and study non-local Jacobi operators, which generalize the classical (local) Jacobi operators. We show that these operators extend to generators of ergodic Markov semigroups with unique invariant probability…
We address the problem of measuring nonclassicality in continuous-variable bosonic systems without having access to a known reference signal. To this end, we construct broader classes of criteria for nonclassicality which allow us to…