Related papers: Some probabilistic trees with algebraic roots
We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the…
The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given `far away' observations. Several theoretical results (and simple algorithms) are available when…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
We consider, for every positive integer $a$, probability distributions on subsets of vertices of a graph with the property that every vertex belongs to the random set sampled from this distribution with probability at most $1/a$. Among…
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,…
In this paper, we study a regular rooted coloured tree with random labels assigned to its edges, where the distribution of the label assigned to an edge depends on the colours of its endpoints. We obtain some new results relevant to this…
To each generic complex polynomial $p(z)$ there is associated a labeled binary tree (here referred to as a "lemniscate tree") that encodes the topological type of the graph of $|p(z)|$. The branching structure of the lemniscate tree is…
We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
Each natural number can be associated with some tree graph. Namely, a natural number $n$ can be factorized as $$ n = p_1^{\alpha_1}\ldots p_k^{\alpha_k},$$ where $p_i$ are distinct prime numbers. Since $\alpha_i$ are naturals, they can be…
A connected graph can be associated with two distinct evolution algebras. In the first case, the structural matrix is the adjacency matrix of the graph itself. In the second case, the structural matrix is the transition probabilities matrix…
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…
Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…
We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…
A classification is given for factorizations of almost simple groups with at least one factor solvable, and it is then applied to characterize $s$-arc-transitive Cayley graphs of solvable groups, leading to a striking corollary: Except the…