Exposé

Finite-sample statistical guarantees for learning dynamical systems in state-space form

Jeudi, 27 novembre 2025 - 10:15 - 11:15

In this talk, I will present an overview of recent results on finite-sample Probably Approximately Correct (PAC) and PAC-Bayesian bounds for learning partially observed dynamical systems in state-space form. For clarity, we begin with linear stochastic systems in discrete time, learned from a single trajectory, and then discuss extensions to more complex nonlinear settings.

On the derivation of mean-curvature flow and its fluctuations from microscopic interactions

On the derivation of mean-curvature flow and its fluctuations from microscopic interactions

Jeudi, 11 septembre 2025 - 11:30 - 12:30

The emergence of mean-curvature flow of an interface between different phases or populations is a phenomenon of long standing interest in statistical physics.  
In this talk, we review recent progress with respect to a class of reaction-diffusion stochastic particle systems on an $n$-dimensional lattice.
In such a process, particles can move across sites as well as be created/annihilated according to diffusion and reaction rates.  
These rates will be chosen so that there are two preferred particle mass density levels $a_1$, $a_2$ in `balance'.

Optimal inference for the mean of random functions

Jeudi, 2 octobre 2025 - 10:15 - 11:15

We study estimation and inference for the mean of real-valued random func- tions defined on a hypercube. The independent random functions are observed on a discrete, random subset of design points, possibly with heteroscedastic noise. We propose a novel optimal-rate estimator based on Fourier series expansions and establish a sharp non-asymptotic error bound in L2−norm.

Local and nonlocal density estimates for variational problems with degenerate double-well potentials

Mardi, 14 octobre 2025 - 11:30 - 12:30

In this seminar we present some recent results regarding density estimates for level sets of minimizers of local and nonlocal energies, which arise from phase separation problems, such as the Ginzburg-Landau energy functional. In particular, we prove density estimates when the phase separation is induced by a double-well potential which presents a slow growth from the pure phases. As a byproduct, we obtain the uniform convergence of the interfaces of any sequence of minimizers of a suitably rescaled energy functional to a set with Hausdorff codimension one.

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