20 citations · 65 across the 19 of their papers we have counts for
24 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…
An alternative approach to large deviations for the almost-critical Erdős-Rényi random graph
Luisa Andreis, Gianmarco Bet, Maxence Phalempin
We study the near-critical behavior of the sparse Erdős-Rényi random graph on vertices, where the connection probability satisfies $np = 1+θ(b_n^2/n)…
Generating synthetic power grids using exponential random graphs models
Francesco Giacomarra, Gianmarco Bet, Alessandro Zocca
Synthetic power grids enable secure, real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel m…
Detecting a late changepoint in the preferential attachment model
Gianmarco Bet, Kay Bogerd, Rui M. Castro +1
Motivated by the problem of detecting a change in the evolution of a network, we consider the preferential attachment random graph model with a time-dependent attachment function.…
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…
Localized geometry detection in scale-free random graphs
Gianmarco Bet, Riccardo Michielan, Clara Stegehuis
We consider the problem of detecting whether a power-law inhomogeneous random graph contains a geometric community, and we frame this as an hypothesis testing problem. More precise…
The financial health of a company and the risk of its default: Back to the future
Gianmarco Bet, Francesco Dainelli, Eugenio Fabrizi
We theorize the financial health of a company and the risk of its default. A company is financially healthy as long as its equilibrium in the financial system is maintained, which…
Metastability of the three-state Potts model with general interactions
Gianmarco Bet, Anna Gallo, Seonwoo Kim
We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants , where are the possible spin values (or c…
Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics
Gianmarco Bet, Anna Gallo, Francesca R. Nardi
We consider the ferromagnetic q-state Potts model on a finite grid graph with non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type…
Metastability for the degenerate Potts Model with negative external magnetic field under Glauber dynamics
Gianmarco Bet, Anna Gallo, Francesca R. Nardi
We consider the ferromagnetic q-state Potts model on a finite grid graph with non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type…
An algorithm to construct subsolutions of convex optimal control problems
Gianmarco Bet, Markus Fischer
We propose an algorithm that produces a non-decreasing sequence of subsolutions for a class of optimal control problems distinguished by the property that the associated Bellman op…
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…
Critical configurations and tube of typical trajectories for the Potts and Ising models with zero external field
Gianmarco Bet, Anna Gallo, Francesca Romana Nardi
We consider the ferromagnetic q-state Potts model with zero external field in a finite volume evolving according to Glauber-type dynamics described by the Metropolis algorithm in t…
Effect of energy degeneracy on the transition time for a series of metastable states: application to Probabilistic Cellular Automata
Gianmarco Bet, Vanessa Jacquier, Francesca R. Nardi
We consider the problem of metastability for stochastic reversible dynamics with exponentially small transition probabilities. We generalize previous results in several directions.…
Limit theorems for Lévy flights on a 1D Lévy random medium
Samuele Stivanello, Gianmarco Bet, Alessandra Bianchi +2
We study a random walk on a point process given by an ordered array of points on the real line. The distances are i.i.d. random variabl…
Weakly interacting oscillators on dense random graphs
Gianmarco Bet, Fabio Coppini, Francesca R. Nardi
We consider a class of weakly interacting particle systems of mean-field type. The interactions between the particles are encoded in a graph sequence, i.e., two particles are inter…
Detecting a botnet in a network
Gianmarco Bet, Kay Bogerd, Rui M. Castro +1
We formalize the problem of detecting the presence of a botnet in a network as an hypothesis testing problem where we observe a single instance of a graph. The null hypothesis, cor…
Weighted Dyck paths for nonstationary queues
Gianmarco Bet, Jori Selen, Alessandro Zocca
We consider a model for a queue in which only a fixed number of customers can join. Each customer joins the queue independently at an exponentially distributed time. Assuming f…
An alternative approach to heavy-traffic limits for finite-pool queues
Gianmarco Bet
We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the…
Big jobs arrive early: From critical queues to random graphs
Gianmarco Bet, Remco van der Hofstad, Johan S. H. van Leeuwaarden
We consider a queue to which only a finite pool of customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement arr…
Finite-pool queues with heavy-tailed services
Gianmarco Bet, Remco van der Hofstad, Johan S. H. van Leeuwaarden
We consider the queue, in which a a total of customers independently demand service after an exponential time. We focus on the case of heavy-tailed service times,…
Heavy-traffic analysis through uniform acceleration of queues with diminishing populations
Gianmarco Bet, Remco van der Hofstad, Johan S. H. van Leeuwaarden
We consider a single server queue that serves a finite population of customers that will enter the queue (require service) only once, also known as the queue. Thi…