Related papers: Iterating random functions on a finite set

Let $t$ be random and uniformly distributed in the interval $[T,2T]$, and consider the quantity $N(t+1/\log T) - N(t)$, a count of zeros of the Riemann zeta function in a box of height $1/\log T$. Conditioned on the Riemann hypothesis, we…

We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number $k$ of real continuous functions $f_1,\cdots, f_k$ such that the functions $f_i\circ T^n$, $n\in\mathbb Z$, $1\leq i\leq k,$ span a…

We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…

Let $\Sigma_{2n}$ be the set of all partitions of the even integers from the interval $(4,2n], n>2,$ into two odd prime parts. We select a partition from the set $\Sigma_{2n}$ uniformly at random. Let $2G_n$ be the number partitioned by…

Selecting N random points in a unit square corresponds to selecting a random permutation. By putting 5 types of symmetry restrictions on the points, we obtain subsets of permutations : involutions, signed permutations and signed…

We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.

The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…

We propose the construction of entire functions with a given random collection of zeros. There are considered two particular cases. In the first one we are dealing with simple zeros. And the second corresponds to random zeros with random…

A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…

Information functionals allow to quantify the degree of randomness of a given probability distribution, either absolutely (through min/max entropy principles) or relative to a prescribed reference one. Our primary aim is to analyze the…

Consider a one dimensional diffusion process on the diffusion interval $I$ originated in $x_0\in I$. Let $a(t)$ and $b(t)$ be two continuous functions of $t$, $t>t_0$ with bounded derivatives and with $a(t)<b(t)$ and $a(t),b(t)\in I$,…

Let X be a countably infinite set of real numbers and let Y_x, x \in X, be an independent family of stationary random subsets of the real numbers, e.g. homogeneous Poisson point processes. We give criteria for the a.s. existence of various…

Let $N_n=\{1,2,...,n\}$. Elements are drawn from the set $N_n$ with replacement, assuming that each element has probability $1/n$ of being drawn. We determine the limiting distributions for the waiting time until the given portion of pairs…

We prove the leading order of a conjecture by Fyodorov, Hiary and Keating, about the maximum of the Riemann zeta function on random intervals along the critical line. More precisely, as $T \rightarrow \infty$ for a set of $t \in [T, 2T]$ of…

Let $S_n$ be the symmetric group of $n$ letters; Landau considered the function $g(n)$ defined as the maximal order of an element of $S_n$. This function is non-decreasing. Let us define the sequence $n_1=1, n_2=2, n_3=3, n_4=4,n_5=5,n_6=7,…

We describe a construction of random meromorphic functions with prescribed simple poles with unit residues at a given stationary point process. We characterize those stationary processes with finite second moment for which, after…

In this paper we develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations. For example, $n+2\to 2n\to 2^n\to…

Consider the set of functions $f_{\theta}(x)=|\theta -x|$ on $\mathbb{R}$. Define a Markov process that starts with a point $x_0 \in \mathbb{R}$ and continues with $x_{k+1}=f_{\theta_{k+1}}(x_{k})$ with each $\theta _{k+1}$ picked from a…

For any continuous probability measure $\mu$ on ${\mathbb R}$ we construct an IFS with probabilities having $\mu$ as its unique measure-attractor.

Let T be a complete, first-order theory in a finite or countable language having infinite models. Let I(T,kappa) be the number of isomorphism types of models of T of cardinality \kappa. We denote by \mu (respectively \hat\mu) the number of…