Schedule

Saturday, May 2, 2026

11:10-12:10

On the entropy of sums in continuous and discrete settings

Abstract: The Entropy Power Inequality (EPI) provides a lower bound on the entropy of the sum of two independent continuous random variables, and has become a central tool connecting probability, information theory, geometry, and analysis. In this talk, we will introduce the background and main ideas behind the EPI, emphasizing its connections to the Central Limit Theorem and to fundamental geometric inequalities. While the continuous theory is comparatively well understood, discrete analogues lead to challenging open problems. We will discuss some of these problems, along with partial results and recent progress, including work toward discrete analogues of the EPI and toward stability results in the continuous setting, where one seeks to understand the structure of distributions that nearly saturate the inequality.

The talk is based on joint works with Matthieu Fradelizi, Ioannis Kontoyiannis and Martin Rapaport.

Lampros Gavalakis
University of Cambridge

12:10-13:00

Coffee Break

13:00-14:00

Diffusion in the random Lorentz gas

Abstract: Since the pioneering works of Hendrik Lorentz (1905) and Paul and Tatiana Ehrenfest (1912) the deterministic (Hamiltonian) motion of a point-like particle exposed to the action of a collection of fixed, randomly located short range scatterers has been a much studied model of physical diffusion under fully deterministic (Hamiltonian) dynamics, with random initial conditions. This model of physical diffusion is known under the name of "random Lorentz gas" or "random wind-tree model". Celebrated milestones on the route to better mathematical understanding of this model of true physical diffusion are the Kinetic Limits for the tagged particle trajectory under the so-called Boltzmann-Grad (a.k.a. low density), or weak coupling approximations [Gallavotti (1970), Spohn (1978), Boldrighini-Bunimovich-Sinai (1982), respectively, Kesten-Papanicolaou (1980)]. Under a second diffusive space-time scaling limit - done as a second step, after the kinetic approximations - the central limit theorem (CLT) and invariance principle (IP) for the tagged particle motion follow. However, the CLT/IP under bare diffusive space-time scaling (without first applying the kinetic approximations) remains a Holy Grail. In recent work we have obtained some intermediate results, partially interpolating between the two-steps-limit (first kinetic, then diffusive - as described above) and the bare-diffusive-limit (Holy Grail). We establish the Invariance Principle for the tagged particle trajectories under a joint kinetic+diffusive limiting procedure, performed simultaneously rather than successively, reaching significantly longer time scales than in earlier works. The Holy Grail (i.e., CLT under bare diffusive scaling) remains, however, beyond reach. I will present a survey of the main problems and (historic and more recent) results.

Balint Tóth
Alfréd Rényi Institute of Mathematics

14:00-15:30

Lunch

15:30-16:30

Learning causal graphs via nonlinear sufficient dimension reduction

Abstract: We introduce a new nonparametric methodology for estimating a directed acyclic graph (DAG) from observational data. Our method is nonparametric in nature: it does not impose any specific form on the joint distribution of the underlying DAG. Instead, it relies on a linear operator on repro- ducing kernel Hilbert spaces to evaluate conditional independence. However, a fully nonparametric approach would involve conditioning on a large number of random variables, subjecting it to the curse of dimensionality. To solve this problem, we apply nonlinear sufficient dimension reduction to reduce the number of variables before evaluating the conditional independence. We develop an estimator for the DAG, based on a linear operator that characterizes conditional independence, and establish the consistency and convergence rates of this estimator, as well as the uniform consistency of the estimated Markov equivalence class. We introduce a modified PC-algorithm to implement the estimating procedure efficiently such that the complexity depends on the sparseness of the un- derlying true DAG. We demonstrate the effectiveness of our methodology through simulations and a real data analysis.

Solea, E., Li, B., & Kim, K. (2025). Learning causal graphs via nonlinear sufficient dimension reduction. Journal of Machine Learning Research, 26(75), 1-46.

Eftychia Solea
Queen Mary University of London

After the last talk, there will be a final coffee break to wrap up and get another chance to chat and say goodbye.

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Speakers

Lampros Gavalakis is a Postdoctoral Research Associate of the EPSRC funded INFORMED-AI program, based at the Department of Pure Mathematics and Mathematical Statistics, at the University of Cambridge. Before that, he was a Postdoctoral Fellow of the MathInGreaterParis program, which is cofunded by the Marie Sklodowska-Curie Actions. He received his Ph.D. from the Engineering Department of the University of Cambridge, where he was working in the Signal Processing and Communications Laboratory, and his undergraduate degree in computer science from Athens University of Economics and Business. He is a recipient of the 2023 Jack Keil Wolf ISIT Student Paper Award. His research interests lie in information theory and probability theory, as well as their connections to additive combinatorics and convex analysis.

Bálint Tóth is Emeritus Professor of Probability at the University of Bristol as well as a research professor at the Alfréd Rényi Institute of Mathematics. He earned his PhD in 1988 from the Hungarian Academy of Sciences and has held senior research and professorial positions in Budapest. His work ranges from microscopic models of Brownian motion and quantum spin systems to limit theorems for random walks with long memory, non-conventional stochastic processes, and hydrodynamic limits. He has made influential contributions to the theory of self-interacting motions (reinforced, self-avoiding, and self-repellent processes) and, with Wendelin Werner, constructed the random geometric object now known as the Brownian web. Tóth has been an invited speaker at ICM 2018 and ECM 2000, and has delivered plenary and featured lectures at major meetings including SPA 2005, SPA 2014, and SPA 2022 (as an IMS Medallion Lecturer). He is a member of Academia Europaea and a corresponding member of the Hungarian Academy of Sciences, and has served in leading editorial roles, including as Editor-in-Chief of the Electronic Journal of Probability and the Annals of Applied Probability. He has served as co-Editor-in-Chief of Probability Theory and Related Fields.

Eftychia Solea is a Lecturer in Statistics in the School of Mathematical Sciences at Queen Mary University of London (QMUL). Before joining QMUL, she held lecturing positions at CREST and ENSAI (Rennes, France), and previously worked as a postdoctoral researcher at Ruhr University Bochum and the University of Cyprus. She received her PhD in Statistics from The Pennsylvania State University. She also earned an MSc in Statistics from Penn State, a Master of Advanced Study (Part III) from the University of Cambridge, and a BSc in Mathematics from the National Technical University of Athens. Her research develops statistical methodology for random functions—mathematical curves viewed as random elements in Hilbert spaces—with applications including medical imaging. She has contributed to graphical models, dimension reduction, quantile regression, and causal inference for functional data, and more recently has expanded into distributional data analysis, where observations are distributions or probability densities.

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