Related papers: Uniform multifractal structure of stable trees

We use the Mass Transport Principle to analyze the local recursion governing the resolvent $(A-z)^{-1}$ of the adjacency operator of unimodular random trees. In the limit where the complex parameter $z$ approaches a given location $\lambda$…

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and $p$-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar…

This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges…

We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these…

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…

The diameter distribution of a given species of deciduous trees in mature, temperate zone forests is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data…

Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…

We compute the magnitude (an isometric invariant of metric spaces) of compact $\mathbb{R}$-trees and show that it equals $1 + L/2$, where $L \in [0, \infty]$ denotes the total length. Although length is the only geometric invariant captured…

We present a graph theoretical approach to the configurational statistics of random tree-like objects, such as randomly branching polymers. In particular, for ideal trees we show that Pr\"ufer labelling provides: (i) direct access to the…

We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest…

A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…

Motivated by the study of random temporal networks, we introduce a class of random trees that we coin \emph{uniform temporal trees}. A uniform temporal tree is obtained by assigning independent uniform $[0,1]$ labels to the edges of a…

A random field composed by Poisson distributed Brownian vortex filaments is constructed. The filament have a random thickness, length and intensity, governed by a measure $\gamma$. Under appropriate assumptions on $\gamma$ we compute the…

We study the properties of time sequences extracted from a self-organized critical system, within the framework of the mathematical multifractal analysis. To this end, we propose a fixed-mass algorithm, well suited to deal with highly…

The properties of scale-free random trees are investigated using both preconditioning on non-extinction and fixed size averages, in order to study the thermodynamic limit. The scaling form of volume probability is found, the connectivity…

There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of pairwise distances between leaves. Such…

We study the typical behavior of the harmonic measure in large critical Galton-Watson trees whose offspring distribution is in the domain of attraction of a stable distribution with index $\alpha\in (1,2]$. Let $\mu_n$ denote the hitting…

We consider fixed-point equations for probability measures charging measured compact metric spaces that naturally yield continuum random trees. On the one hand, we study the existence/uniqueness of the fixed-points and the convergence of…

We define decorated $\alpha$-stable trees which are informally obtained from an $\alpha$-stable tree by blowing up its branchpoints into random metric spaces. This generalizes the $\alpha$-stable looptrees of Curien and Kortchemski, where…

We evaluate the scale at which the multifractal structure of some random Gibbs measures becomes discernible. The value of this scale is obtained through what we call the growth speed in H\"older singularity sets of a Borel measure. This…