Related papers: Permutations, moments, measures
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two…
By a classical principle of analysis, sufficiently thin subsequences of general sequences of functions behave like sequences of independent random variables. This observation not only explains the remarkable properties of lacunary…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
We use moment method to understand the cycle structure of the composition of independent invariant permutations. We prove that under a good control on fixed points and cycles of length 2, the limiting joint distribution of the number of…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
We present a family of explicit formulae for evaluating absolute moments of probability measures on $\mathbb{R}^d$ in terms of Fourier transforms. As to the space of probability measures possessing finite absolute moments of an arbitrary…
A generalized Catalan matrix $(a_{n,k})_{n,k\ge 0}$ is generated by two seed sequences $\mathbf{s}=(s_0,s_1,\ldots)$ and $\mathbf{t}=(t_1,t_2,\ldots)$ together with a recurrence relation. By taking $s_\ell=2\ell+1$ and $t_\ell=\ell^2$ we…
Dokos et. al. studied the distribution of two statistics over permutations $\mathfrak{S}_n$ of $\{1,2,\dots, n\}$ that avoid one or more length three patterns. A permutation $\sigma\in\mathfrak{S}_n$ contains a pattern…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed…
This paper introduces the notion of measure representation of DNA sequences. Spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes. The main aim of this paper is…
In this paper we give a bijection between the class of permutations that can be drawn on an X-shape and a certain set of permutations that appears in [Knuth] in connection to sorting algorithms. A natural generalization of this set leads us…
The aim of this paper is to study the full $K-$moment problem for measures supported on some particular non-linear subsets $K$ of an infinite dimensional vector space. We focus on the case of random measures, that is $K$ is a subset of all…
We analyse q-functional equations arising from tree-like combinatorial structures, which are counted by size, internal path length, and certain generalisations thereof. The corresponding counting parameters are labelled by a positive…
We examine the distribution and popularity of different parameters (such as the number of descents, runs, valleys, peaks, right-to-left minima, and more) on the sets of increasing and flattened permutations. For each parameter, we provide…
We define multideterminantal probability measures, a family of probability measures on $[k]^n$ where $[k]=\{1,2,\dots,k\}$, generalizing determinantal measures (which correspond to the case $k=2$). We give examples coming from the positive…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
The normalized factorial moments $F_q$ are continued to noninteger values of the order $q$, satisfying the condition that the statistical fluctuations remain filtered out. That is, for Poisson distribution $F_q = 1$ for all $q$. The…