Related papers: The moment problem for random objects in a categor…
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region…
Given a multi-index sequence $\mu_{\mathbf{k}}$, $\mathbf{k} = (k_1,..., k_n) \in \mathbb{N}_0^n$, necessary and sufficient conditions are given for the existence of a regular Borel polymeasure $\gamma$ on the unit interval $I= [0,1]$ such…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
The Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly an infinite family of probability densities with the same sequence of moments. In this paper, the notion of $q$-moment…
Let $f$ be a Gaussian random field on $\mathbb{R}^d$ and let $X$ be the number of critical points of $f$ contained in a compact subset. A long-standing conjecture is that, under mild regularity and non-degeneracy conditions on $f$, the…
The problem of characterising the accuracy of, and disturbance caused by a joint measurement of position and momentum is investigated. In a previous paper the problem was discussed in the context of the unbiased measurements considered by…
The problem of what moments can exist for the coding radius of a finitary map between two i.i.d. processes, has been extensively studied in the case of $\mathbb{Z}$-processes. Here we treat this problem for factor maps between…
The purpose of this paper is to study the problem of estimating a compactly supported density of probability from noisy observations of its moments. In fact, we provide a statistical approach to the famous Hausdorff classical moment…
The generalized moment problem (GMP) is an infinite dimensional linear problem over the cone of finite nonnegative Borel measures. When a GMP instance involves finitely many polynomial moment constraints, moment/sum-of-squares hierarchies…
The problem of guessing subject to distortion is considered, and the performance of randomized guessing strategies is investigated. A one-shot achievability bound on the guessing moment (i.e., moment of the number of required queries) is…
This paper shows that the problem of testing hypotheses in moment condition models without any assumptions about identification may be considered as a problem of testing with an infinite-dimensional nuisance parameter. We introduce a…
This paper treat determinacy of strong moment problems in part I and indeterminacy of strong moment problems in part II. This paper is a summary of the following papers: [1] Ald\'en. E., Determinacy of Strong Moment Problems. [2] On…
When p divides the ordering of Galois group, the distribution of the Sylow p-subgroup of Cl(K) is closely related to the problem of counting fields with certain specifications. Moreover, different orderings of number fields affect the…
The points of a moment variety are the vectors of all moments up to some order of a family of probability distributions. We study this variety for mixtures of Gaussians. Following up on Pearson's classical work from 1894, we apply current…
Cosmological fine-tuning has traditionally been associated with the narrowness of the intervals in which the parameters of the physical models must be located to make life possible. A more thorough approach focuses on the probability of the…
Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…
Probability densities that are not uniquely determined by their moments are said to be "moment-indeterminate", or "M-indeterminate". Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is…
The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose…
We consider the counting function of ideals in a given ideal class of a number field of degree $d$. This describes, at least conjecturally, the Fourier coefficients of an automorphic form on $\text{GL}(d)$, typically not a Hecke eigenform…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…