NOTE: All seminars are held in person at the Department of Mathematics in Via Carlo Alberto 10, Turin.
Second semester 2025/2026
Upcoming seminars:
Wed 6 May, 2026. Sala Orsi, 14:15-15:15
Elena Magnanini (WIAS Berlin)
Title: Limit theorems for homogeneous and inhomogeneous ERGMs
Abstract: Exponential Random Graphs are a class of network models that can be seen as the generalization of the dense Erdős–Rényi random graph. They are defined, with a statistical mechanics approach, by introducing a Hamiltonian, a function that biases the occurrence of certain features, such as the number of edges or triangles. In this talk we will primarily focus on the so-called edge triangle model, where the Hamiltonian of the system only collects edge and triangle densities, properly tuned by real parameters. Using tools from statistical mechanics and large deviation theory, we establish limit theorems and concentration inequalities for subgraph densities (mainly focusing on edge and triangle density) in the replica-symmetric regime, where the limiting free energy of the model is known together with its phase diagram. Part of the results are concerned with a mean-field approximation, which allows for explicit computations and provides insights into the behavior of the original model in certain parameter region where rigorous results are hardly achievable. A generalization of the model in which vertices are allowed to carry a type will also be discussed.
This talk is based on joint work with A. Bianchi, F. Collet, and G. Passuello.
Wed 13 May, 2026. Aula 5, 09:30-10:30
Costantino Ricciuti (Sapienza - Università di Roma)
Title: On some kinetic limits leading to non-Markovian random flights and anomalous diffusions
Abstract: Well-known models in kinetic theory (such as those related to the Boltzmann equation) aim to explain, in a mathematically rigorous way, how mechanical interactions between particles at the microscopic level can, through scaling limits, produce the macroscopic behavior of a gas. Many current results focus on diffusive macroscopic behavior, while anomalous diffusion and non-Markovian models have been comparatively less explored.
In our work [2], we consider a Lorentz gas, that is, we analyze the motion of a particle moving among fixed obstacles. Under suitable assumptions on the distribution of these obstacles, a kinetic limit leads to a non-Markovian random flight with long-range dependence, whose flight times form a set of exchangeable variables. A further scaling limit yields anomalous diffusion.
This situation differs from that considered by Gallavotti [1] and Spohn [4], where, by choosing other distributions of the obstacles, one obtains a Markovian random flight and diffusive behavior.
We then develop a theory for a class of non-Markovian processes with long-range dependence and exchangeable waiting times and study their governing equations, which turn out to be nonlocal in both time and space (see [2] and [3]).
[1] G. Gallavotti, Rigorous Theory of the Boltzmann Equation in the Lorentz Gas, Nota interna n. 358, Istituto di Fisica, Università di Roma, 1972.
[2] Facciaroni, L., Ricciuti, C., Scalas, E., & Toaldo, B. (2025). Random Flights and Anomalous Diffusion: A Non-Markovian Take on Lorentz Processes. arXiv preprint arXiv:2507.02796.
[3] Facciaroni, L., Ricciuti, C., & Scalas, E. (2026). Non-Markovian chains with long-range dependence and their scaling limits. arXiv preprint arXiv:2602.23049.
[4] Spohn, H. (1978). The Lorentz process converges to a random flight process. Communications in Mathematical Physics, 60(3), 277-290.
Past seminars:
Mon 30 March, 2026. Aula 1, Palazzo Campana, 11:30-12:30
Lucio Galeati (Universitá dell'Aquila)
Title: Fluctuations for mean field limits of singular particle systems driven by fBm
Abstract: We consider a system of $N$ particles, subject to a mean-field type pairwise interaction kernel $K$, each driven by an independent fractional Brownian motion (idiosyncratic noises). Previous works established that, for a large class of non-Lipschitz, possibly singular kernels, the associated McKean-Vlasov equation is well-posed, and the empirical measure converges to its law as $N\to\infty$, with rate of order $N^{-1/2}$ in suitable negative Sobolev norms. In this talk I will present results concerning the Gaussian fluctuations underlying this mean field convergence, validating the optimality of this rate; they are valid for both first order interactions and for kinetic systems. The proofs are based on the use of Girsanov transform and the method of U-statistics first introduced by Sznitman.
Based on ongoing joint work with Avi Mayorcas (Bath) and Johanna Weinberger (Technion).
Thu 2 April, 2026. Aula 1, Palazzo Campana, 14:00-15:00
Laura Perelli (Università degli studi di Milano)
Title: Mean field optimal stopping with uncontrolled state
Abstract: We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems arise, for instance, in the pricing of American options when the underlying asset follows a McKean-Vlasov dynamics. Due to the time inconsistency of these problems, we provide a suitable reformulation of the original problem for which a dynamic programming principle can be established. To accomplish this, we first enlarge the state space and then introduce the so-called extended value function. We prove that the Snell envelope of the original problem can be written in terms of the extended value function, from which we can derive a characterization of the smallest optimal stopping time. On the enlarged space, we restore time-consistency and in particular establish a dynamic programming principle for the extended value function. Finally, by employing the notion of Lions measure derivative, we derive the associated Hamilton-Jacobi-Bellman equation, which turns out to be a second-order variational inequality on the product space [0, T] × Rd × P2(Rd); under suitable assumptions, we prove that the extended value function is a viscosity solution to this equation.
Wed 22 April, 2026. Aula 1, 14:30-15:30
Mattia Martini (École Polytechnique)
Title: PDEs driven by Dirichlet-Ferguson laplacian in Wasserstein-Sobolev spaces
Abstract: In this talk, we discuss linear and nonlinear PDEs defined on the space of probability measures over the flat torus, equipped with the Dirichlet-Ferguson measure. We first present an analytic framework based on the Wasserstein-Sobolev space associated with the Dirichlet form induced by the infinite-dimensional Laplacian acting on functions of measures. Within this setting, we establish existence and uniqueness results for transport-diffusion and Hamilton-Jacobi equations in the Wasserstein space. Our analysis connects the PDE approach with a corresponding interacting particles system providing a probabilistic (Kolmogorov-type) representation of strong solutions. Finally, we extend the theory to semilinear equations and mean-field type optimal control problems, together with consistent finite-dimensional approximations.
First semester 2025/2026
Wed 29 October, 2025. Sala S, Palazzo Campana, 12:00-13:00
Mladen Savov (Sofia University)
Title: The inverse first-passage time problem for stochastic processes including Lévy processes and diffusions
Abstract: In this talk we consider the inverse first-passage time problem which consists in determining whether for a given positive random variable and a stochastic process X there is a deterministic curve such that the passage of X above it has the law of the given positive random variable. We discuss the existence and the uniqueness of those curves for arbitrary positive random variables. We exemplify our results for Lévy processes and diffusions.
This is joint work with Alexander Klump.
Wed 19 November, 2025. Sala Orsi, Palazzo Campana, 12:00-13:00
Ivana Valentić (University of Zagreb)
Title: Excursion theory for the Wright--Fisher diffusion
Abstract: The Wright--Fisher diffusion is one of the most prominent forwards-in-time models used within mathematical population genetics to describe the way in which population-level allele frequencies change over time. It falls outside the usual scope of general diffusion theory in several ways: its diffusion coefficient vanishes and fails to be Lipschitz-continuous at the boundary of its domain. In this talk I will present an excursion-based construction of the neutral Wright--Fisher diffusion. Diffusions with a single boundary point are natural subjects for excursion theory because all excursions begin and end at a single point, facilitating a Markovian construction of a path from concatenated excursions. Excursions of processes from more general sets have also been described, but the results are rarely tractable because it is in general not clear how to concatenate the resulting excursions into a path. Our construction is intermediate between these two regimes, featuring excursions which always start from a specified point, and end at one of two boundary points which determine the next starting point. (Based on work with: P. A. Jenkins, J. Koskela, V.M. Rivero, J. Sant and D. Spanò)
Wed 28 January, 2026. Aula 4, Palazzo Campana, 12:15-13:15
Michał Gutowski (Bulgarian Academy of Sciences and Sofia University)
Title: Trapping effect of stable processes
Abstract: We are interested in the motion of a particle in a disordered medium, where the local structure of the environment induces random trapping events whose intensity depends on the particle’s position. We model this phenomenon by a $\beta$-stable process subordinated by the inverse of a $\alpha(x)$-stable subordinator, where $\beta\in(1,2]$. The resulting process is semi-Markovian. We will see that under appropriate technical assumptions on the function $\alpha(x)$, the process spends only a negligible amount of time outside a neighbourhood of the set of $\mathrm{arg\,min\,\alpha(x)}$.
The work is a natural continuation of the results provided by M. Savov and B. Toaldo in Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation, Ann. Inst. Henri Poincaré Probab. Stat., 56(4): 2640 – 2671, 2020.
Thu 5 February, 2026. Aula 4, Palazzo Campana, 12:00-13:00
Seonwoo Kim (Yonsei University)
Title: Transience time of the subcritical facilitated exclusion process
Abstract: In this talk, we consider the facilitated exclusion process on the one-dimensional discrete N-torus. Because of the facilitating mechanism, the process freezes in finite time if the particle density of the initial configuration is subcritical, i.e., if it is smaller than (or equal to) 1/2. We prove that, starting from any subcritical Bernoulli product measure, the correct scale of the transience/freezing time is of order \log^3N. Based on a joint work with Oriane Blondel, Clément Erignoux and Sanha Lee.
Organized by
Bruno Toaldo: bruno.toaldo@unito.it
Elena Issoglio: elena.issoglio@unito.it
Luisa Andreis: luisa.andreis@unito.it
Sponsors
Department of Mathematics "Giuseppe Peano", University of Torino