36 citations · 143 across the 37 of their papers we have counts for
43 papers
Raphaël Cerf
We discuss the famous conjecture {} for the Bernoulli site percolation model on with . We prove that, for , in the Bernoulli percol…
The case of equality in BK
Raphaël Cerf, Pierre Tesio
We characterize the pairs of increasing events for which there is equality in the BK inequality. Namely, we show that if and only if all the configurat…
The pivotal set of a Boolean function
Raphaël Cerf
We define the pivotal set of a Boolean function and we prove a fundamental inequality on its expected size, when the inputs are independent random coins of parameter~. We give t…
Survival of the flattest in the quasispecies model
Maxime Berger, Raphaël Cerf
Viruses present an amazing genetic variability. An ensemble of infecting viruses, also called a viral quasispecies, is a cloud of mutants centered around a specific genotype. The s…
A martingale minimax exponential inequality for Markov chains
Raphaël Cerf
We prove a new inequality controlling the large deviations of the empirical measure of a Markov chain. This inequality is based on the martingale used by Donsker and Varadhan and t…
The time constant for Bernoulli percolation is Lipschitz continuous strictly above
Raphaël Cerf, Barbara Dembin
We consider the standard model of i.i.d. first passage percolation on given a distribution on ( is allowed). When $G([0,+\infty]) < p_c(d)…