Related papers: Random hyperbolic graphs in $d+1$ dimensions
In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space ($R^d$ with a metric of indefinite signature). We show that a…
We study the distribution of the set of copies of some given graph $H$ in the random graph $G(n,p)$, focusing on the case when $H = K_r$. Our main results capture the 'leading term' in the difference between this distribution and the…
Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in…
While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
This document is an informal bibliography of the papers dealing with distributed approximation algorithms. A classic setting for such algorithms is bounded degree graphs, but there is a whole set of techniques that have been developed for…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…
Superbubbles are acyclic induced subgraphs of a digraph with single entrance and exit that naturally arise in the context of genome assembly and the analysis of genome alignments in computational biology. These structures can be computed in…
The paper addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic…
The progress in hyperbolic neural networks (HNNs) research is hindered by their absence of inductive bias mechanisms, which are essential for generalizing to new tasks and facilitating scalable learning over large datasets. In this paper,…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
We study the systole of a random surface, where by a random surface we mean a surface constructed by randomly gluing together an even number of triangles. We study two types of metrics on these surfaces, the first one coming from using…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
In one dimension, any disorder is traditionally believed to localize all states. We show that this paradigm breaks down under hyperuniform disorder, which suppresses long-wavelength fluctuations and interpolates between random and periodic…
We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no…
We prove limit theorems for the greatest common divisor and the least common multiple of random integers. While the case of integers uniformly distributed on a hypercube with growing size is classical, we look at the uniform distribution on…