2026 - 2027 Program

Title: The number of descendants in a preferential attachment graph. 

Speaker: Tiffany Y. Y. Lo, Stockholm University, Sweden  (video, slides).

Abstract: We study the number $X^{(n)}$ of vertices that can be reached from the last added vertex $n$ via a directed path (the descendants) in the standard preferential attachment random graph. In this model, vertices are sequentially added, each born with out-degree $m> 2$; the endpoint of each outgoing edge is chosen among previously added vertices with probability proportional to the current degree of the vertex plus some number $\rho$. We show that $X^{(n)}/n^\nu$ converges in distribution as $n\to\infty$, where $\nu$ depends on both $m$ and $\rho$, and the limiting distribution is given by a product of a constant factor and the $(1-\nu)$-th power of a Gamma(m/(m − 1), 1) variable. I will discuss the main result and some aspects of the proof. 

Joint work with Svante Janson. 

Title: Ornstein-Uhlenbeck operators induced by the  Berezin-Weyl-Segal-Bargmann-Fock models.

Speaker: Jendoubi Souheyl, University Tunis Elmanar, Tunisia.

Abstract:  Let G be a non-compact connected and simply connected nilpotent Lie subgroup of GLn(C) acting holomorphically on the Euclideancomplex plane C and having an irreducible unitary representation (Tg)g∈G on the reproducing kernel Hilbert space of holomorphic functions HL2(C, dμ), where μ is a probability measure on C and let ρ de-notes the innitesimal representation associated to Tg. We prove that each quintuple (G,C, Tg, ρ, μ) induces naturally an Ornstein-Uhlenbeck operator (phenomenon) analog to the Langevin stochastic dynamics. Moreover, we study the perturbation of these operators in some equivalent models. We illustrate our study by considering unitary holomorphic representations of the Heisenberg group H3 = C × R and the Engel group G4 in the Berezin-Weyl-Segal-Bargmann-Fock models.

Title: Local time penalizations with various clocks for Lévy processes.

Speaker:  Kouji Yano, University of Osaka, JAPAN. 

Abstract: For one-dimensional Lévy processes, we discuss local time penalizations, a generalization of conditioning to avoid zero. The limits are taken via certain families of random times, called clocks.

The limit processes may differ according to the choice of the clocks when the original Lévy process is recurrent and of finite variance.

This talk is based on a joint work with Shosei Takeda (Electron. J. Probab., 28, 1--35, 2023).

Title: How long does it take to train an Elephant Random Walk? 

Speaker:  Zheng Fang, University of Zurich, Switzerland.

Abstract: We study how conditioning on the first $k$ steps, which we think of as training, affects the long-term behavior of the Elephant Random Walk. When the elephant is conditioned to be at position $k$ at time $k$, the first return time to the origin scales as $k^{(4-4p)/(3-4p)}$ in the diffusive regime, and grows exponentially in the critical regime. We loosely interpret this as a measurement of the rate at which the elephant forgets its training. 

Title:  Co-evolution of Vertex Opinions and Edge Dynamics in Random Graphs.

Speaker: Siva Athreya, International Institute for Theoretical Sciences, India.

Abstract: A pressing challenge in network statistics lies in understanding systems with two simultaneous levels of dynamics: randomly evolving processes on randomly evolving networks locked in a feedback loop — a setting termed co-evolution that creates complex bi-directional interactions.

We will propose a  model on a dynamically evolving graph in which vertices can change opinions and edges can switch between being present or absent in a coupled way. We will work towards a complete mathematical description of a class of mutually coupled opinion dynamics and graph dynamics in the large-size limit and  also explore when consensus and polarisation may occur in the population.

This is joint work with Frank den Hollander and Adrian Roellin 

Title: Optimal Intervention in Natural Resource and Energy Markets: Infinite-Horizon Stochastic Impulse Control with Random Coefficients.

Speaker: Helmi Zaatra, Qatar university, Qatar.

Abstract: Decision-makers in natural resource and financial markets must repeatedly decide when and how much to intervene under uncertainty, random coefficients, and possible execution delays. This talk presents a unified probabilistic approach to infinite-horizon stochastic impulse control, motivated by energy production markets. Because the underlying dynamics are non-Markovian and reward functions may be random, classical quasi-variational inequality methods do not apply. We rely on the Snell envelope and reflected backward stochastic differential equations (BSDEs). We construct an iterative approximation scheme based on strategies with a bounded number of impulses, prove convergence and continuity of the value process, and establish the existence of an optimal impulse control, including the case with a fixed execution delay and one pending order. We also extend the analysis to the risk-sensitive case via exponential utility. A numerical example illustrates the optimal trade-off between intervention costs and long-term profitability in oilfield well management. This talk is based on two joint works with Boualem Djehiche, Said Hamadene, and Ibtissem Hdhiri (2021), DOI: 10.1287/moor.2021.1145,  and  DOI: 10.3934/jdg.2026013 

Title: Estimates on escape times for the elephant random walk.

Speaker: Morgan André, Universidade de Sao Paulo, Brasil.

Abstract:   We study the gambler’s ruin problem for the Elephant Random Walk, focusing on escape time from a symmetric interval of the form {−N, . . . , N}. As our main result, we derive tight exponential bounds for the tail of this escape time. We then illustrate the usefulness of such bounds by proving that, in the diffusive regime, the Elephant’s average behavior mirrors that of the traditional symmetric random walk: the expected escape time grows quadratically with N. 

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Speaker: Nacira Agram, KTH Royal Institute of Technology, Sweden.

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Title: From Signs to Matrices on Edges: Generalising Structural Balance on Networks.

Speaker: Renaud Lambiotte, University of Oxford, United Kingdom. 

Abstract:  Structural balance is a classical notion in network science, originally introduced in social psychology to describe globally consistent patterns of positive and negative relations. Here we present an overview of a series of works that progressively generalise this concept from signed graphs to richer classes of weighted networks. Starting from weighted signed networks, where each edge carries a real value with a sign, we revisit the classification into balanced, antibalanced, and strictly unbalanced regimes, and show how each is reflected in spectral properties and in the behaviour of spreading processes and other dynamics. We then extend the framework to networks whose edges are weighted by complex numbers, replacing the binary sign with a continuous phase, and further to matrix-weighted networks, where interactions act on multidimensional states through matrix couplings. In all these settings, the same fundamental principle applies: balance, or more generally coherence, describes whether signals propagating along different paths combine coherently or destructively interfere. This unifying viewpoint connects structural consistency to the spectrum of generalised adjacency and Laplacian matrices, and thereby to the long-term behaviour of both linear and nonlinear dynamics. We illustrate the reach of this perspective through consensus dynamics, random walks, spectral clustering, and synchronisation of higher-dimensional Kuramoto oscillators on networks.

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Speaker: Krishanu Maulik, Indian Statistical Institute, India.

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Speaker:  Salim A. Messaoudi, University of Sharjah, United Arab Emirates.

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Speaker: Leonidas Kordalis, University of Athens, Greece.

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Speaker:  Minmin Wang, University of Sussex , United Kingdom. 

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