Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Cerf, Raphael"'
Autor:
Cerf, Raphaël
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~$p$. We give two complete proofs of this inequality. Along the way, we obtain the cl
Externí odkaz:
http://arxiv.org/abs/2405.19541
Autor:
Cerf, Raphaël, Mariconda, Carlo
The basic problem of the calculus of variations consists of finding a function that minimizes an energy, like finding the fastest trajectory between two points for a point mass in a gravity field moving without friction under the influence of gravity
Externí odkaz:
http://arxiv.org/abs/2404.02901
Autor:
Berger, Maxime, Cerf, Raphaël
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 simplest model of evolution, whose equilibrium state is described by th
Externí odkaz:
http://arxiv.org/abs/2306.09221
Autor:
Cerf, Raphaël
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 the minimax theorem. It holds for convex sets and it requires to take a
Externí odkaz:
http://arxiv.org/abs/2211.04856
Autor:
Cerf, Raphaël, Dembin, Barbara
We consider the standard model of i.i.d. first passage percolation on $\mathbb{Z}^d$ given a distribution $G$ on $[0,+\infty]$ ($+\infty$ is allowed). When $G([0,+\infty]) < p_c(d)$, it is known that the time constant $\mu_G$ exists. We are intereste
Externí odkaz:
http://arxiv.org/abs/2101.11858
In this paper we consider the Glauber dynamics for the one-dimensional Ising model with dissipation, in a mesoscopic regime obtained by letting inverse temperature and volume go to infinity with a suitable scaling. In this limit the magnetization has
Externí odkaz:
http://arxiv.org/abs/2002.08244
Autor:
Cerf, Raphaël, Forien, Nicolas
Publikováno v:
ALEA, Lat. Am. J. Probab. Math. Stat. 19, 367-416 (2022)
We consider the Bernoulli percolation model in a finite box and we introduce an automatic control of the percolation probability, which is a function of the percolation configuration. For a suitable choice of this automatic control, the model is self
Externí odkaz:
http://arxiv.org/abs/1912.06639
Autor:
Cerf, Raphaël, Dembin, Barbara
We consider the anchored isoperimetric profile of the infinite open cluster, defined for $p > p\_c$, whose existence has been recently proved in [3]. We extend adequately the definition for $p = p\_c$, in finite boxes. We prove a partial result which
Externí odkaz:
http://arxiv.org/abs/1903.08065
Autor:
Cerf, Raphaël, Zhou, Wei
We consider the Bernoulli bond percolation model in a box $\Lambda$ (not necessarily parallel to the directions of the lattice) in the regime where the percolation parameter is close to $1$. We condition the configuration on the event that two opposi
Externí odkaz:
http://arxiv.org/abs/1811.12368
Autor:
Berestycki, Nathanael, Cerf, Raphael
We study a self-attractive random walk such that each trajectory of length $N$ is penalised by a factor proportional to $\exp ( - |R_N|)$, where $R_N$ is the set of sites visited by the walk. We show that the range of such a walk is close to a solid
Externí odkaz:
http://arxiv.org/abs/1811.04700