Hybrid seminar at McGill University or Zoom.

With the conceptual aim of optimizing Markov chains in one way or another for better mixing, we analyze them on random directed graphs according to a multitype configurational model. We review the toolkit we build upon, focusing on the evolution of the entropy of the path of the walk developed by Bordenave, Caputo, Salez(2018), originally for simple random walks on random directed graphs without types. Then we allow tuning the transition probabilities corresponding to the types. Our goal is to understand the impact on mixing achieved through this flexibility, together with the observed cutoff phenomenon. Joint work with John Fernley.

Bio: Balázs Gerencsér received the M.Sc. and Ph.D. degrees in mathematics from Eötvös Loránd University, in 2007 and 2013, respectively. He was a Visiting Student Researcher at LIDS at MIT, with the support of a Fulbright Scholarship, in 2009-2010, then a Research Assistant with the Alfréd Rényi Institute of Mathematics, in 2011-2013. After graduation, he held a postdoctoral position at Université catholique de Louvain, 2013-2015. He then returned to Alfréd Rényi Institute of Mathematics, tenured in 2020, and is also an Assistant Professor at Eötvös Loránd University.