Related papers: A Kolmogorov Consistency Theorem in the Multiple P…

We adapt arguments concerning entropy-theoretic convergence from the independent case to the case of FKG random variables. FKG systems are chosen since their dependence structure is controlled through covariance alone, though in the sequel…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

In this paper we define the closure under weak convergence of the class of p-tempered {\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element…

In this paper we show that the closure of a random sample for a k-dimensional random vector is almost surely a deterministic set of all heavy points of the distribution. A heavy point is defined to be a point for which all its neighborhoods…

We prove for outer continuous belief measures defined on compact spaces strong and weak laws of large numbers as Kolmogorov's one for measures. These results contribute to M. Marinacci's (Journal of Economic Theory 84 (1999) 145-195) though…

We discuss several tests for whether a given set of independent and identically distributed (i.i.d.) draws does not come from a specified probability density function. The most commonly used are Kolmogorov-Smirnov tests, particularly…

Non-compact symmetries cannot be fully broken by randomness since non-compact groups have no invariant probability distributions. In particular, this makes trickier the "Copernican" random choice of the place of the observer in infinite…

This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…

Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…

This paper derives the asymptotic distribution of variance weighted Kolmogorov-Smirnov statistics for conditional moment inequality models for the case of a one dimensional covariate. The asymptotic distribution depends on the data…

We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…

Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…

We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…

Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a…

We prove in a direct fashion that a multidimensional probability measure is determinate if the higher dimensional analogue of Carleman's condition is satisfied. In that case, the polynomials, as well as certain proper subspaces of the…

We adapt the definition of the Vietoris map to the framework of finite topological spaces and we prove some coincidence theorems. From them, we deduce a Lefschetz fixed point theorem for multivalued maps that improves recent results in the…

We present a complexity measure for any finite time series. This measure has invariance under any monotonic transformation of the time series, has a degree of robustness against noise, and has the adaptability of satisfying almost all the…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…

The study of the dynamics of an holomorphic map near a fixed point is a central topic in complex dynamical systems. In this paper we will consider the corresponding random setting: given a probability measure $\nu$ with compact support on…