Related papers: Random self-similar series over a rotation
In recent years various results about locally symmetric manifolds were proven using probabilistic approaches. One of the approaches is to consider random manifolds by associating a probability measure to the space of discrete subgroups of…
We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables…
We study loop near-rings, a generalization of near-rings, where the additive structure is not necessarily associative. We introduce local loop near-rings and prove a useful detection principle for localness.
Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is,…
This paper is inspired by the problem of understanding in a mathematical sense the Liouville quantum gravity on surfaces. Here we show how to define a stationary random metric on self-similar spaces which are the limit of nice finite…
The random percolation model can be viewed as the dual of a well defined confining gauge theory; since this theory, having no Monte Carlo dynamics at all, is simple to simulate, it is possible to study the properties of the flux tube with…
The formation of spacetime singularities is a quite common phenomenon in General Relativity and it is regulated by specific theorems. It is widely believed that spacetime singularities do not exist in Nature, but that they represent a…
A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…
This article studies regularity properties of multiplicative stochastic processes on infinite-dimensional Lie groups. We investigate conditions under which these processes admit c\`adl\`ag modifications and derive bounds on their local…
We consider the bounds imposed by naturalness on the masses of superpartners for arbitrary points in nonminimal supersymmetric extensions of the standard model and for arbitrary messenger scales. This constitutes a significant…
In this paper, we study the dynamical uniform boundedness principle over a family of rational maps with certain nontrivial automorphisms. Specifically, we consider a family of rational maps of an arbitrary degree $d\ge 2$ whose automorphism…
The paper investigates the properties of a nonlinear recursive sequence which includes several ones studied formerly in the literature.
We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application of natural boundaries in determining asymptotic results.
The main result of this paper is an analogue for a continuous family of tori of Kronecker-Weyl's unique ergodicity of irrational rotations. We show that the notion corresponding in this setup to irrationality, namely asynchronicity, is…
We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matrices are automatic. This shows a new relation between two…
We study the properties of rotation numbers for some groups of piecewise linear homeomorphisms of the circle. We use these properties to obtain results on PL rigidity, non isomorphicity, non exoticity of automorphisms, non smoothability for…
Double circulant matrices are introduced and studied. A formula to compute the rank r of a double circulant matrix is exhibited; and it is shown that any consecutive r rows of the double circulant matrix are linearly independent. As a…
We consider skew product extension of irrational rotations on the circle by $\Z^2$ determined by an integer valued function as well as a fixed point on the circle. We study ergodic components of such extension.
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
We study discrete-time random dynamical systems where each fibre map is an orientation-preserving homeomorphism of the circle. We prove that the existence of a random periodic cycle with period at least two implies that the random rotation…