Wandering on random digraphs
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János Pach [1]
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[1] EPFL Lausanne and Rényi Institute Budapest
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- Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 6-6
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
Random walks on random graphs is an active area of research with numerous results in the last 20 years.While the theory is well developed for undirected graphs, the directed case is much less understood.Unfortunately, networks that arise in applications are often directed by nature (e.g. World Wide Web,citation network, ...). In recent years, new techniques have been developed to study the directed setting.In this talk I will survey some of the most prominent results in the area, including the study of therandom stationary measure and the mixing properties of the chain. Time permitting, I will cover twotopics more in-depth. First, I will show how directed edges dramatically increase the time requiredto visit every vertex of the graph. Second, I will present a mathematical framework for the so-called‘power-law hypothesis’, a property relating in-degrees with Pagerank – the webpage ranking at the coreof Google’s search engine.The results presented are joint work with Xing Shi Cai, Pietro Caputo and Matteo Quattropani.
