162 citations · 1.3k across the 49 of their papers we have counts for
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On the long time behavior of the TCP window size process
Djalil Chafai, Florent Malrieu, Katy Paroux
The TCP window size process appears in the modeling of the famous Transmission Control Protocol used for data transmission over the Internet. This continuous time Markov process ta…
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 fine properties of mixtures with respect to concentration of measure and Sobolev type inequalities
Djalil Chafai, Florent Malrieu
Mixtures are convex combinations of laws. Despite this simple definition, a mixture can be far more subtle than its mixed components. For instance, mixing Gaussian laws may produce…