13 papers
Stable Coexistence in Ecologies and Games
Türkü Özlüm Çelik, Vincenzo Antonio Isoldi, Irem Portakal +1
We study feasible stable equilibria of Lotka-Volterra systems and their higher-order extensions. We complete the classification of impossible ecological interaction networks with a…
Colorful Exponential Random Graph Models
Bhaswar B. Bhattacharya, Pierfrancesco Dionigi, Ankan Ganguly +1
In this paper, we initiate the study of colored exponential random graph models (ERGMs), a class of exponential-family models for networks with multiple types of edge relations. Us…
Markov and lattice bases for Forman-Ricci curvature of graphs
Jane Ivy Coons, Giulio Zucal
Discrete Forman-Ricci curvature is a quantity associated to each edge of a graph that describes its local geometry. It has proven to be a useful tool in network analysis in a varie…
Spectral theory of dense hypergraph limits
Ágnes Backhausz, Christian Kuehn, Sjoerd van der Niet +2
In this work, we develop a spectral theory for hypergraph limits. We prove the convergence of the spectra of adjacency and Laplacian matrices for hypergraph sequences converging in…
Large deviations for probability graphons
Pierfrancesco Dionigi, Giulio Zucal
We establish a large deviation principle (LDP) for probability graphons, which are symmetric functions from the unit square into the space of probability measures. This notion exte…
Strata of Ecological Coexistence via Grassmannians
Türkü Özlüm Çelik, Pierre A. Haas, Georgy Scholten +2
We study the Lotka--Volterra system from the perspective of computational algebraic geometry, focusing on equilibria that are both feasible and stable. These conditions stratifies…
Probability graphons and P-variables: two equivalent viewpoints for dense weighted graph limits
Giulio Zucal
We develop further the graph limit theory for dense weighted graph sequences. In particular, we consider probability graphons, which have recently appeared in graph limit theory as…
Probability graphons: the right convergence point of view
Giulio Zucal
We extend the theory of probability graphons, continuum representations of edge-decorated graphs arising in graph limits theory, to the 'right convergence' point of view. First of…
Exploring the space of graphs with fixed discrete curvatures
Michelle Roost, Karel Devriendt, Giulio Zucal +1
Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and th…
Action convergence of general hypergraphs and tensors
Giulio Zucal
Action convergence provides a limit theory for linear bounded operators where are potentially different probability spaces. This…
There is no going back: Properties of the non-backtracking Laplacian
Raffaella Mulas, Dong Zhang, Giulio Zucal
We prove new properties of the non-backtracking graph and the non-backtracking Laplacian for graphs. In particular, among other results, we prove that two simple graphs are isomorp…
A measure-theoretic representation of graphs
Raffaella Mulas, Giulio Zucal
Inspired by the notion of action convergence in graph limit theory, we introduce a measure-theoretic representation of matrices, and we use it to define a new notion of pseudo-metr…
Stochastic Rotating Waves
Christian Kuehn, James MacLaurin, Giulio Zucal
Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems th…