arXiv subjects

Paul de Buyer

Publications and source records attributed to Paul de Buyer.

4 recordsLinked to original sources

arXiv2018

A proof of the Bunkbed conjecture on the complete graph for $p\geqslant1/2$

The bunkbed of a graph $G$ is the graph $G\times\left\{ 0,1\right\} $. It has been conjectured that in the independent bond percolation model, the probability for $\left(u,0\right)$ to be connected with $\left(v,0\right)$ is greater than the probability for $\left(u,0\right)$ to be connected with $\left(v,1\right)$, for any vertex $u$, $v$ of $G$. In this article, we prove this conjecture for the complete graph in the case of the independent bond percolation of parameter $p\geqslant1/2$.

math.PR↗

arXiv2017

A Note on Helffer-Sjöstrand Representation for a Ginzburg-Landau Process

In this work, we explore a link between an unbounded spin system given by a system of stochastic differential equations and a random walk. This allows us to study the decay of the (co)variance of functions with respect to time. We extend here the previous work of T. Bodineau and G. Graham to a more general class of graph and potential.

math.PR↗

arXiv2016

A proof of the bunkbed conjecture for the complete graph at $p=\frac{1}{2}$

The bunkbed of a graph $G$ is the graph $G\times K_2 $. It has been conjectured that in the independent bond percolation model, the probability for $\left(u,0\right)$ to be connected with $\left(v,0\right)$ is greater than the probability for $\left(u,0\right)$ to be connected with $\left(v,1\right)$, for any vertex $u$, $v$ of $G$. In this article, we prove this conjecture for the complete graph in the case of the independent bond percolation of parameter $p=1/2$.

math.CO↗

arXiv2015

Diffusive Decay of the Environment Viewed by the Particle

We prove an optimal diffusive decay of the environment viewed by the particle in random walk among random independent conductances, with, as a main assumption, finite second moment of the conductance. Our proof, using the analytic approach of Gloria, Neukamm and Otto, is very short and elementary.

math.PR↗