nm - Research

Research interests

I work at the intersection of probability theory, combinatorics and statistical physics, occassionally drawing tools from statistics, data science, machine learning and computer science. My main interest is developing and studying mathematical foundations of complex networks, through the lens of universality. Specifically, I want to better understand:

Universal structural and statistical aspects of complex networks.
Opinion dynamics and spreading processes (e.g., formation of consensus in a population).
Random optimization problems and their algorithmic aspects, such as limitations of efficient algorithms in finding optimal solutions (statistical-computational gaps).

Papers

[* indicates undergraduate (at the time) co-author]

Estimating Community Boundaries in Geometric Random Graphs, with Taha Ameen. (submitted) [arxiv]

Finding Adam in noisy trees, with Luc Devroye and Gábor Lugosi. (submitted) [arxiv]

Multipartite random graphs with given degrees: local limit, revisiting the giant, distances. (submitted) [arxiv]

Algorithmic Phase Transition for Large Independent Sets in Dense Hypergraphs, with Abhishek Dhawan, Nhi U. Dinh*, Eren C. Kızıldağ, Bayram A. Şahin. [arxiv] Extended abstract published at APPROX/RANDOM 2026. [extended abstract]

On exponentially height-penalized random trees, with Louigi Addario-Berry, Benoît Corsini and Meltem Ünel. (submitted) [arxiv]

Evolution of recursive trees with limited memory, with Omer Angel, Shankar Bhamidi, Serte Donderwinkel and Akshay Sakanaveeti. (accepted with minor revisions at Annales de l'Institut Henri Poincaré B: Probabilités et Statistiques) [arxiv]

On random bipartite graphs evolving by degrees. (submitted) [arxiv]

Sharp Online Hardness for Large Balanced Independent Sets, with Abhishek Dhawan and Eren C. Kızıldağ. (submitted) [arxiv]

Annealed Potts models on Rank-1 inhomogeneous random graphs, with Cristian Giardinà, Claudio Giberti, Remco van der Hofstad and Guido Janssen. (submitted) [arxiv]

Condensation in scale-free geometric graphs with excess edges, with Remco van der Hofstad, Pim van der Hoorn, Céline Kerriou and Peter Mörters. Annals of Applied Probability, 2026 [arxiv] [journal]

Long-range competition on the torus, with Bas Lodewijks. (to appear in Annals of Applied Probability) [arxiv] [talk video (at BIRS-CMI workshop on network models, December 2024, Chennai)]

See also Bas' webpage for a nice simulation

Scaling of the Clustering Function in Spatial Inhomogeneous Random Graphs, with Remco van der Hofstad and Pim van der Hoorn. Journal of Statistical Physics, 2023 [arxiv] [journal]

Local limits of Spatial Inhomogeneous Random Graphs, with Remco van der Hofstad and Pim van der Hoorn. Advances in Applied Probability, 2023 [arxiv] [journal]

Theses

Doctoral thesis: Structural properties and competition on random graphs with underlying geometry. [link]
MS thesis: Random Graphs with Given Degree Sequence. [link]

Coauthors: Taha Ameen, Omer Angel, Louigi Addario-Berry, Shankar Bhamidi, Benoît Corsini, Luc Devroye, Abhishek Dhawan, Nhi U. Dinh, Serte Donderwinkel, Cristian Giardinà, Claudio Giberti, Remco van der Hofstad, Pim van der Hoorn, Guido Janssen, Céline Kerriou, Eren C. Kızıldağ, Bas Lodewijks, Gábor Lugosi, Peter Mörters, Bayram A. Şahin, Akshay Sakanaveeti, Meltem Ünel.

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