162 citations · 848 across the 46 of their papers we have counts for
4 papers · 2 filters
Spectrum of large random reversible Markov chains: two examples
Charles Bordenave, Pietro Caputo, Djalil Chafai
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…
Circular Law Theorem for Random Markov Matrices
Charles Bordenave, Pietro Caputo, Djalil Chafai
Consider an nxn random matrix X with i.i.d. nonnegative entries with bounded density, mean m, and finite positive variance sigma^2. Let M be the nxn random Markov matrix with i.i.d…
On the birth-and-assassination process, with an application to scotching a rumor in a network
Charles Bordenave
We give new formulas on the total number of born particles in the stable birth-and-assassination process, and prove that it has an heavy-tailed distribution. We also establish that…
Resolvent of Large Random Graphs
Charles Bordenave, Marc Lelarge
We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and derive…