Aida Abiad (Eindhoven University of Technology & Vrije Universiteit Brussel)

Spectral approach to Kemeny’s constant

Kemeny’s constant, a fundamental parameter in the theory of Markov chains, has recently received significant attention within the graph theory community. Originally defined for a discrete, finite, time-homogeneous, and irreducible Markov chain based on its stationary vector and mean first passage times, Kemeny’s constant finds special relevance in the study of random walks on graphs. Kemeny’s constant gives a measure of how quickly a random walker can move around a graph and is thus a good measure of the connectivity of a graph. Kemeny’s constant has many useful interpretations, including the spread of infectious diseases (how quickly a disease will reach epidemic levels), molecular conformation dynamics (presence or absence of metastable sets), and urban road networks (how well connected a network is). For these and other applications, the main question is: how do changes in the network lead to changes in Kemeny’s constant? In this talk we investigate the effect of the network structure on Kemeny’s constant. We do so by showing several new approximations for Kemeny’s constant, which we derive using spectral techniques.

Biography

Aida Abiad is an associate professor at the Department of Mathematics and Computer Science at Eindhoven University of Technology, The Netherlands. She received her PhD from Tilburg University in 2015, and had appointments at Maastricht University, Ghent University and Vrije Universiteit Brussel. Her main research interests are in algebraic combinatorics and its application to other fields such as coding theory or quantum information theory. She serves on the editorial board of the open access journals The Electronic Journal of Combinatorics and The Electronic Journal of Linear Algebra. She is a recipient, among other awards, of a FWO research fellowship and a NWO Vidi fellowship. Since 2024, she has been also appointed part-time associate professor at the Vrije Universiteit Brussel.

Christoph Brune (University of Twente)

To be announced