My work uses probability, graph-limit theory, spectral methods and ideas from statistical mechanics to study large random systems. A recurring theme is the relationship between microscopic constraints or interactions and the macroscopic structures that emerge in large networks.
Probability graphons, weighted networks and large deviations
Probability graphons extend classical graphons by assigning a probability distribution, rather than a single binary edge value, to each pair of latent vertex positions. They provide a common language for weighted, coloured, multiplex and distribution-valued dense networks. With Giulio Zucal, I established a large-deviation principle for random weighted graphs in this space.
Large deviations for probability graphons
Exponential random edge-coloured graphs
In ongoing joint work with Bhaswar Bhattacharya, Ankan Ganguly and Giulio Zucal, I study dense edge-coloured exponential random graph models through probability graphons. The framework turns asymptotic free energies into entropy-penalised variational problems and provides a route to typical structures and extremal colourings.
Exponential random edge-coloured graphs
Stochastic processes on large random graphs
With Dániel Keliger, I study how random graph topology and initial conditions affect the accuracy of mean-field approximations for Markov processes on networks. The results distinguish generic initial conditions from sufficiently homogeneous ones and identify different error scales.
Mean-field approximations on random graphs
Spectral signatures of ensemble equivalence
A research line developed during my PhD compares hard-constraint and soft-constraint random graph ensembles through their principal eigenvalues. It covers constrained regular graphs, Chung–Lu random graphs and the configuration model.
Spectral random graphs and ensemble equivalence
Preferential attachment and evolving networks
Recent joint work introduces quantum preferential attachment, in which a new node may connect near a chosen target rather than necessarily to the target itself. This local flexibility produces two classes of small-world networks, neither scale-free.
Quantum preferential attachment
Non-exchangeable interacting particle systems
During a 2026 research stay at the Barcelona School of Economics with Chiara Amorino, I began studying interacting particle systems whose heterogeneous interactions are represented through probability graphons. This is ongoing work at the interface of non-exchangeable mean-field systems, graph limits and statistical inference.
Other ongoing collaborations
- Large deviations for the Village Model, with L. Andreis, J. Komjáthy and B. Ráth.
- Large deviations for subgraph counts in directed sparse random graphs, with A. Arras.
- Network methods for ceramic technology in archaeology, with E. Kroon, A. Ferraro, D. Garlaschelli and T. Gili.
Research interests
Graph limits (graphon theory, action convergence, local–global convergence, local weak limits) · large deviations for graph limits, graph ensembles and metastable states · stochastic processes on random graphs and their mean-field descriptions · statistical physics, Ising and spin-glass models · preferential attachment with non-Markovian attachment schemes · mixing times for Glauber dynamics · random matrix theory applied to graph theory · Gibbs ensembles for random graphs (exponential random graph models).
Given my education in theoretical physics, I retain a strong interest in applications of probability theory to physics and to interdisciplinary fields such as economics and the social sciences, with a more recent interest in data science, machine learning and their mathematical foundations.
See the publications page for the full list, and applied work for the quantitative side.