Spectrum of large random reversible Markov chains: two examples

Understand

We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment.

• As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior at the edge, including the so called spectral gap.
• Results are obtained for two simple models with distinct limiting features.
• The first model is built on the complete graph while the second is a birth-and-death dynamics.