Related papers: Characterization of distributions whose forward di…
We construct a random model to study the distribution of class numbers in special families of real quadratic fields $\mathbb Q(\sqrt d)$ arising from continued fractions. These families are obtained by considering periodic continued…
We study divisibility properties of a set $\{f_1(\mathbf{U}_n^{(s)}),\ldots,f_m(\mathbf{U}_n^{(s)})\}$, where $f_1,\ldots,f_m$ are polynomials in $s$ variables over $\mathbb{Z}$ and $\mathbf{U}_n^{(s)}$ is a point picked uniformly at random…
Mellin moments of off-forward distribution functions are even polynomials of the skewedness parameter. This constraint, called polynomiality property, follows from Lorentz- and time-reversal invariance. We prove that the unpolarized…
Let $X$ be a real-valued random variable with distribution function $F$. Set $X_1,\dots, X_m$ to be independent copies of $X$ and let $F_m$ be the corresponding empirical distribution function. We show that there are absolute constants…
Recent innovations on the differential calculus for functions of non-commuting variables, begun for a quaternionic variable, are now extended to the case of a general matrix over the complex numbers. The expansion of F(X+Delta) is given to…
We investigate the fluctuations and large deviations of the root of largest modulus in a model of random polynomial with independent complex Gaussian coefficients (Kac polynomials). The fluctuations were recently computed by R. Butez (arxiv…
In the first part of this paper we establish, in terms of so called k-tangential sets, a kind of optimal estimate for the size and structure of the set of non-differentiability of Lipshitz functions with one-sided directional derivatives.…
The complex exponentials with integer frequencies form a basis for the space of square integrable functions on the unit interval. We analyze whether the basis property is maintained if the support of the complex exponentials is restricted…
For the family $P:=x^n+a_1x^{n-1}+\cdots +a_n$ of complex polynomials in the variable $x$ we study its {\em discriminant} $R:=$Res$(P,P',x)$, $R\in \mathbb{C}[a]$, $a=(a_1,\ldots ,a_n)$. When $R$ is regarded as a polynomial in $a_k$, one…
The function spaces of continuously differentiable functions are extensively studied and appear in various mathematical settings. In this context, we investigate the spaces of continuously fractional differentiable functions of order…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…
We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…
Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by…
We study large deviation properties of probability distributions with either a compact support or a fat tail by comparing them with q-deformed exponential distributions. Our main result is a large deviation property for probability…
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gau{\ss} count the remaining ones, approximately and exactly. For polynomials in two or more…
We study some constructions on distributions in a uniform $p$-adic context, and also in large positive characteristic, using model theoretic methods. We introduce a class of distributions which we call distributions of ${\mathscr…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
We study fluctuations of polynomial linear statistics for discrete Schr\"odinger operators with a random decaying potential. We describe a decomposition of the space of polynomials into a direct sum of three subspaces determining the growth…
Mellin moments of off-forward distribution functions are, at t = 0, even polynomials of the skewedness parameter xi. It is proven that the unpolarized off-forward distribution functions in the chiral quark soliton model satisfy this so…