Research
Research interests
My research focuses on probability theory and interacting particle systems. I am interested in:
coagulation processes;
condensation, gelation and phase transitions;
interacting random walks and scaling limits;
reinforced processes;
emergence of self-sustained periodic behaviour in cooperative systems;
mean-field interacting particle systems and propagation of chaos;
large deviations.
Coauthors (in alphabetical order):
Andrea Agazzi, Amine Asselah, David Barbato, Gianmarco Bet, Francesca Collet, Paolo Dai Pra, Markus Fischer, Maria Flora, Fulvio Fontini, Marco Formentin, Tejas Iyer, Wolfgang König, Heide Langhammer, Elena Magnanini, Elisa Marini, Robert I. A. Patterson, Maxence Phalempin, Federico Polito, Luigi Provenzano, D. R. Michiel Renger, Laura Sacerdote, Daniele Tovazzi, Tiziano Vargiolu
Publications
L. A., D. Barbato, F. Collet, M. Formentin, L. Provenzano, Strong existence and uniqueness of the stationary distribution for a stochastic inviscid dyadic model, Nonlinearity (2016).
L. A., F. Polito, L. Sacerdote, On a class of Time-fractional Continuous-state Branching Processes, Markov processes and related fields (2017).
L. A., P. Dai Pra, M. Fischer, Simultaneous jumps in interacting particle systems: from neuronal networks to a general framework, Mathematical and Computational Neuroscience: cell, network and data analysis, Springer INdAM series, 2017.
L.A., D. Tovazzi, Coexistence of stable limit cycles in a generalized Curie-Weiss model with dissipation, J Stat Phys (2018).
L. A., P. Dai Pra, M. Fischer, McKean-Vlasov limit for interacting systems with simultaneous jumps, Stochastic Analysis and Applications (2018).
L.A., A. Asselah, P. Dai Pra, Ergodicity of a system of interacting random walks with asymmetric interaction, Annales de l'Institut Henri Poincare (B) Probability and Statistics (2019).
L.A., M. Flora, F. Fontini, T. Vargiolu, Pricing Reliability Options under different electricity price regimes, Energy Economics, 2020.
L.A., W. König, R.I.A. Patterson, A large-deviations principle for all the cluster sizes of a sparse Erdős-Rényi graph, Random Structures and Algorithms (2021).
A. Agazzi, L. A., R. I. A. Patterson, D. R. M. Renger, Large deviations for Markov jump processes with uniformly diminishing rates, Stochastic Processes and their Applications (2022).
L.A., W. König, H. Langhammer, R.I.A. Patterson, A large-deviations principle for all the components in a sparse inhomogeneous random graph, Probability Theory and Related Fields (2023) 186:521–620
Elisa Marini, L. A., Francesca Collet, Marco Formentin, Noise-induced periodicity in a frustrated network of interacting diffusions, Nonlinear Differ. Equ. Appl. NoDEA (2023) 30:34
Preprints
L. A., T. Iyer, E. Magnanini, Gelation, hydrodynamic limits and uniqueness in cluster coagulation processes (2023), arXiv preprint arXiv:2308.10232
L.A., G. Bet, M. Phalempin, An alternative approach to large deviations for the almost-critical Erdős-Rényi random graph (2023), arXiv preprint arXiv:2312.16941
L.A., W. König, H. Langhammer, R.I.A. Patterson, Spatial particle processes with coagulation: Gibbs-measure approach, gelation and Smoluchowski equation (2024), arXiv preprint arXiv:2401.06668