2025 - 2026 Program

Title: On the relative multifractal analysis of branching random walk on Galton-Watson tree.

Speaker: Najmeddine Attia, Department of Mathematics and Statistics, College of Science, King Faisal University, Saudi Arabia.( slides, video)

Abstract: We compute almost surely and simultaneaously the Hausdorff and packing dimensions of the sets of infinite branches of the boundary of a super-critical GaltonWatson tree along which the averages of a vector valued branching random walk have a given set of limit points. This goes beyond multifractal analysis, for which we complete the previous works on the subject by considering the sets associated with levels in the boundary of the domain of study. Our method is inspired by some approach used to solve similar questions in the different context of hyperbolic dynamics for the Birkhoff averages of continuous potentials. It also exploits ideas from multiplicative chaos and percolation theories, which are used to estimate the lower Hausdorff dimension of a family of inhomogeneous Mandelbrot measures. 

Title: Where do random trees grow leaves? 

Speaker: Alessandra Caraceni,  Scuola Normale Superiore di Pisa, Italy.(slides, video)

Abstract: Consider the problem of growing a binary tree uniformly at random by the leaves, that is, of coupling a uniform random binary tree with n internal vertices with a uniform binary tree with one extra internal vertex, in such a way that the latter is obtained from the former by growing two new children of a random leaf. The existence of a probability measure on the leaves for which this uniform growth procedure is possible is due to Łuczak and Winkler, and some more information about what this measure must look like was obtained in joint work with Alexandre Stauffer. With Nicolas Curien and Robin Stephenson, we extend this uniform growth procedure to the continuous setting of the Brownian Tree, and explore the interesting multifractal properties of the resulting leaf growth measure. 

Title: Gaussian fluctuations for the two urn model 

Speaker: Konrad Kolesko, Mathematical Institute, University of Wrocław, Poland.( slides, video)

Abstract:  In my talk, I will present a modification of the classical Pólya urn model, where balls are drawn from one urn and placed into another. We are interested in a limit theorem for a fixed color. I will show that, after subtracting the appropriate leading (and subleading) terms, the difference exhibits Gaussian fluctuations. The talk is based on a joint work with Ecaterina Sava-Huss. 

Title:  Asymptotic behavior of some strongly critical decomposable 3-type Galton–Watson processes with immigration.

Speaker: Dániel Bezdány, Bolyai Institute, University of Szeged, Aradi vertanuk tere  1, H–6720 Szeged, Hungary. (slides, video)

Abstract: We study the asymptotic behavior of a critical decomposable 3-type Galton-Watson processes with immigration whose offspring mean matrix is triangular with diagonal entries 1. Under second or fourth order moment assumptions on the offspring and immigration distributions, we establish a functional limit theorem for the sequence of appropriately scaled

processes. The coordinate processes of the limit process may be described as independent squared Bessel processes and iterated integral processes of their linear combinations. In the proofs we use limit theorems for martingale differences towards a diffusion process due to Ispány and Pap (2010). 

Based on a joint work with Mátyás Barczy,

available at ArXiv: https://arxiv.org/abs/2406.09852.

Title: Limit Profiles for reversible Markov chains. 

Speaker: Evrydiki Xenia Nestoridi, Stony Brook University, Stony Brook NY 11794-3651, USA. (slides, video)

Abstract: A central question in Markov chain mixing is the occurrence of cutoff, a phenomenon according to which a Markov chain converges abruptly to the stationary measure. The focus of this talk is the limit profile of a Markov chain that exhibits cutoff, which captures the exact shape of the distance of the Markov chain from stationarity. We will discuss techniques for determining the limit profile and its continuity properties under appropriate conditions. 

Title: Functional limit theorems for elephant random walks on general periodic structures.

Speaker: Shuhei Shibata, Joint Graduate School of Mathematics for Innovation (JGMI), Kyushu University. (slides, video)

Abstract: Elephant Random Walk (ERW)  is a non-Markovian stochastic process that retains complete memory of its past, making it a fundamental model for studying reinforcement in stochastic processes. In this talk, we extend the analysis of ERWs beyond the classical lattice $\mathbb{Z}^d$ to general periodic structures, including triangular and hexagonal lattices, and we establish functional limit theorems for ERW on them. Our results reveal new structure-dependent quantities that do not appear in the classical setting $\mathbb{Z}^d$, highlighting how the underlying structure affects the asymptotic behavior of the walk. We also present the phenomenon of infinite collisions between two independent ERWs on the integer lattice $\mathbb{Z}$. 

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Speaker: Tameem Amani, Research Scientist - Saudi Aramco. (slides, video)

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Title: Universal approximation for functions of infinite-dimensional signatures.

Speaker: Asma Khedher, University of Amstredam, , The Netherlands.

Abstract: The goal of this work is to establish a universal approximation theorem (UAT) for continuous functionals on the signatures of infinite-dimensional continuous weakly geometric rough paths.  To this end, we apply the Stone–Weierstrass theorem, exploiting the fact that norm-bounded sets are compact in the weak* topology. Our motivation is to use this result for the approximation

 of stochastic partial differential equations, with potential applications to modeling and pricing forward rates within the Heath–Jarrow–Morton-Musiela framework.

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Speaker: Manal Alotibi, King Fahd University of Petroleum & Minerals, KSA.

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Speaker:  Federico Sau, University of Milan, Italy.

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Speaker: Yadh Hafsi, University of Paris-Sacly, France. 

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Speaker:  Colin McSwiggen, Institute of Mathematics, Academia Sinica, Taiwan.

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Speaker:  Ibtissem Hdhiri, University of Gabes, Tunisia.

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Title:  Fast calibration of FARIMA models with dependent errors.

Speaker: Youssef Esstafa,  Le Mans University, France. (slides, video)

Abstract: In this work, we investigate the asymptotic properties of Le Cam’s one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily independent nor martingale differences errors. We show under some regularity assumptions that the one-step estimator is strongly consistent and asymptotically normal with the same asymptotic variance as the least squares estimator. We show through simulations that the proposed estimator reduces computational time compared with the least squares estimator.

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