Related papers: Dimensions of random affine code tree fractals
We introduce a technique that uses projection properties of fractal percolation to establish dimension conservation results for sections of deterministic self-similar sets. For example, let $K$ be a self-similar subset of $\mathbb{R}^2$…
We study the fundamental question of how likely it is that two randomly chosen trees are isomorphic to each other for different models of random trees. We show that the probability decays exponentially for rooted labeled trees as well as…
A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure…
In this article, we study a simple random walk on a decorated Galton-Watson tree, obtained from a Galton-Watson tree by replacing each vertex of degree $n$ with an independent copy of a graph $G_n$ and gluing the inserted graphs along the…
We study a variant of the Falconer distance problem for dot products. In particular, for fractal subsets $A\subset \mathbb{R}^n$ and $a,x\in \mathbb{R}^n$, we study sets of the form \[ \Pi_x^a(A) := \{\alpha \in \mathbb{R} : (a-x)\cdot y=…
The self-similar structure of the attracting subshift of a primitive substitution is carried over to the limit set of the repelling tree in the boundary of Outer Space of the corresponding irreducible outer automorphism of a free group.…
We study a special case of the vertex splitting model which is a recent model of randomly growing trees. For any finite maximum vertex degree $D$, we find a one parameter model, with parameter $\alpha \in [0,1]$ which has a so--called…
We implement numerical techniques to simulate D-random feuilletages, candidates for higher-dimensional random geometries introduced in L. Lionni and J.-F. Marckert, Math. Phys. Anal. Geom. 24 (2021) 39. Using finite-size scaling techniques,…
A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson…
This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are…
We consider a (random permutation model) binary search tree with n nodes and give asymptotics on the loglog scale for the height H_n and saturation level h_n of the tree as n\to\infty, both almost surely and in probability. We then consider…
This paper is devoted to parameter estimation for partially observed polynomial state space models. This class includes discretely observed affine or more generally polynomial Markov processes. The polynomial structure allows for the…
For random matrices with tree-like structure there exists a recursive relation for the local Green functions whose solution permits to find directly many important quantities in the limit of infinite matrix dimensions. The purpose of this…
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of…
We destroy a finite tree of size $n$ by cutting its edges one after the other and in uniform random order. Informally, the associated cut-tree describes the genealogy of the connected components created by this destruction process. We…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
The classes of tree permutations and forest permutations were defined by Acan and Hitczenko (2016). We study random permutations of a given length from these classes, and in particular the number of occurrences of a fixed pattern in one of…
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
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 find precise asymptotic estimates for the number of planar maps and graphs with a condition on the minimum degree, and properties of random graphs from these classes. In particular we show that the size of the largest tree attached to…