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Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph

Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph

We consider the random reversible Markov kernel K obtained by assigning i.i.d. nonnegative weights to the edges of the complete graph over n vertices and normalizing by the corresponding row sum. The weights are assumed to be in the domain of attraction of an α-stable law, α ∈ (0, 2). …