Related papers: Random iterations of homeomorphisms on the circle
In this paper, we introduce and study the iterates of the following family of functions $\varphi_k$ defined on natural numbers which exhibits nice properties. $$\varphi_k(x)=\left\lbrace \begin{array}{ll} x+k, & \mbox{ if $x$ is prime;}\\…
Consider a continuous one parameter family of circles in complex plane that contains two circles lying in the exterior of one another. Under mild assumptions on the family, we prove that if a continuous function on the union of the above…
An approach to modelling random sets with locally finite perimeter as random elements in the corresponding subspace of $L^1$ functions is suggested. A Crofton formula for flat sections of the perimeter is shown. Finally, random processes of…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
In this paper we present a systematic study of continuous local iterated function systems. We prove local iterated function systems admit compact attractors and, under a contractivity assumption, construct their code space and present an…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…
Let $\{f_\nu\}$ be a sequence of holomorphic self-maps of a hyperbolic Riemann surface $X$. In this paper we shall study the asymptotic behavior of the sequences obtained by iteratively left-composing or right-composing the maps…
We present a generalisation of the theory of iterated function systems and associated fractals to the setting of noncommutative geometry. Along the way, we discuss some ideas surrounding locally compact noncommutative metric spaces.
Let $(X,d)$ be a compact metric space, and let an iterated function system (IFS) be given on $X$, i.e., a finite set of continuous maps $\sigma_{i}$: $ X\to X$, $i=0,1,..., N-1$. The maps $\sigma_{i}$ transform the measures $\mu $ on $X$…
This paper considers the egodicity properties in iterated function systems. First, we will introduce chain mixing and chain transitive iterated function systems then some results and examples are presented to compare with these notions in…
We study the law of random self-similar series defined above an irrational rotation on the Circle. This provides a natural class of continuous singular non-Rajchman measures.
The attractors of iterated function systems are usually obtained as the Hausdorff limit of any non-empty compact subset under iteration. In this note we show that an iterated function system on a boundedly compact metric space has compact,…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…