2026 - 2027 Program

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

Speaker: Tiffany Y. Y. Lo, Stockholm University, Sweden.

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. 

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Speaker: Jendoubi Souheyl, University Tunis Elmanar, Tunisia.

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Speaker:  Kouji Yano, The University of Osaka, JAPAN. 

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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 

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Speaker: Helmi Zaatra, Qatar university, Qatar.

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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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Speaker: Krishanu Maulik, Indian Statistical Institute, India.

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

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