6 papers
Dimension properties of a family of random self-similar iterated function systems
Vilma Orgoványi, Károly Simon
In this note we present a dimension formula for certain randomized self-similar sets. The self-similar sets we are considering are -dimensional generalizations of rational proje…
Two-scale branching functions and inhomogeneous attractors
Vilma Orgoványi, Alex Rutar
We introduce the notion of a two-scale branching function associated with an arbitrary metric space, which encodes the lower and upper box dimensions as well as the Assouad spectru…
On the uniformity and size of microsets
Richárd Balka, Vilma Orgoványi, Alex Rutar
We resolve a few questions regarding the uniformity and size of microsets of subsets of Euclidean space. First, we construct a compact set with Assouad dimen…
Interior points and Lebesgue measure of overlapping Mandelbrot percolation sets
Vilma Orgoványi, Károly Simon
We consider a special one-parameter family of d-dimensional random, homogeneous self-similar iterated function systems (IFSs) satisfying the finite type condition. The object of ou…
Multitype branching processes in random environments with not strictly positive expectation matrices
Vilma Orgoványi, Károly Simon
It is well known that under some conditions the almost sure survival probability of a multitype branching processes in random environment is positive if the Lyapunov exponent corre…
Projections of the random Menger sponge
Károly Simon, Vilma Orgoványi
Using a similar random process to the one which yields the fractal percolation sets, starting from the deterministic Menger sponge we get the random Menger sponge. We examine its o…