相关论文: Random fractals and tree-indexed Markov chains
To any rooted tree, we associate a sequence of numbers that we call the logarithmic factorials of the tree. This provides a generalization of Bhargava's factorials to a natural combinatorial setting suitable for studying questions around…
It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in…
The article considers classification task of fractal time series by the meta algorithms based on decision trees. Binomial multiplicative stochastic cascades are used as input time series. Comparative analysis of the classification…
The multifractal structure underlying a self-similar measure stems directly from the weighted self-similar system (or weighted iterated function system) which is used to construct the measure. This follows much in the way that the dimension…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
We introduce a simple tree growth process that gives rise to a new two-parameter family of discrete fragmentation trees that extends Ford's alpha model to multifurcating trees and includes the trees obtained by uniform sampling from…
We consider a fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from…
In this paper we propose a new model of random graph directed fractals that extends the current well-known model of random graph directed iterated function systems, $V$-variable attractors, and fractal and Mandelbrot percolation. We study…
A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…
We develop a theory of Rauzy fractals for random substitutions, which are a generalisation of deterministic substitutions where the substituted image of a letter is determined by a Markov process. We show that a Rauzy fractal can be…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local "random-to-front" reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the…
In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the…
We introduce an algorithm for generating a random sequence of fragmentation trees, which we call the ancestral branching algorithm. This algorithm builds on the recursive partitioning structure of a tree and gives rise to an associated…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…
The theory of resource distribution in self-organizing systems on the basis of the fractal-cluster method has been presented. In turn, the fractal-cluster method is based on the fractal-cluster relations of V.P. Burdakov and the analytical…
Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…
We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not…
We work out the theory of fractional isomorphism of graphons as a generalization to the classical theory of fractional isomorphism of finite graphs. The generalization is given in terms of homomorphism densities of finite trees and it is…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…