Saloff-Coste received his "doctorat de 3eme cycle" in 1983 at the Pierre and Marie Curie University, Paris VI.

[1] In the 1990s, he worked as "Directeur de Recherche" (CNRS) at Paul Sabatier University in Toulouse.

Saloff-Coste works in the areas of analysis and probability theory, including problems involving geometry and partial differential equations.

In particular, he has studied the behavior of diffusion processes on manifolds and their fundamental solutions, in connection to the geometry of the underlying spaces.

He has developed quantitative estimates for the convergence of finite Markov chains and corresponding stochastic algorithms.