10 papers
Renormalisation of Inhomogeneous Random Graphs
Luca Avena, Diego Garlaschelli, Rajat Subhra Hazra +1
We consider inhomogeneous random graphs in which vertices are assigned i.i.d.\ random weights, pairs of distinct vertices are connected by an edge independently with a probability…
Counterintuitive problems in discrete probability
Luca Avena, Gianmarco Bet, Bernardo Busoni
This manuscript contains a collection of counterintuitive problems in discrete probability, together with detailed solutions. The dataset was constructed as part of a broader resea…
How reliable are LLMs when it comes to playing dice?
Luca Avena, Gianmarco Bet, Bernardo Busoni
We investigate the probabilistic reasoning capabilities of large language models through a controlled benchmarking study on discrete probability problems. We constructed two datase…
Network node immunization: improving Netshield algorithm through random rooted forests
Luca Avena, Alexandre Gaudillière, Irina Gurewitsch +2
We are interested in the so-called multiple-node immunization problem for complex networks under attack by a viral agent. It consists in identifying and removing a set of nodes of…
node2vec or triangle-biased random walks: stationarity, regularity & recurrence
Luca Avena, Gianmarco Bet, Lars Schroeder +1
The node2vec random walk is a non-Markovian random walk on the vertex set of a graph, widely used for network embedding and exploration. This random walk model is defined in terms…
Semicircle laws with combined variance for non-uniform ErdÅs-Rényi hypergraphs
Luca Avena, Elia Bisi, Eleonora Bordiga
We consider ErdÅs-Rényi-type random hypergraphs that are non-uniform, in the sense that hyperedges of different sizes may coexist, and inhomogeneous, in that connection probabili…