5 papers
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…
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…
First-order asymptotics for the structure of the inhomogeneous random graph
Gianmarco Bet, Kay Bogerd, Vanessa Jacquier
In the inhomogeneous random graph model, each vertex is assigned a weight , and an edge between any two vertices is present with…
Asymptotic normality of degree counts in a general preferential attachment model
Simone Baldassarri, Gianmarco Bet
We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms connections. The neighbors of the new verte…