Guest Speaker: Goran Nakerst, University of Dresden
Abstract
Continuous-time Markovian processes are commonly used to model complex multi-state systems in various fields, including physics, chemistry, biology, economics, and game theory. These processes are fully determined by their generators. Typical rather than system-specific properties of the generators are perceived by investigating random ensembles of generators.
In this talk, I will focus on spectral properties of generators of Markov processes and their connection to random matrix theory. I will introduce an ensemble of sparse random generators and demonstrate that the sparsity leads to a closure of the large spectral gap typically present in dense random generator ensembles. I will also discuss how the spectral boundary of a paradigmatic model, the asymmetric simple exclusion process, can be related to the cycle structure of random graphs.
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