54 citations · 130 across the 8 of their papers we have counts for
10 papers
On the one-arm probability for the metric graph Gaussian free field in high dimensions
Pierre-François Rodriguez, Jialu Shi, Wen Zhang
We consider the sign clusters of the Gaussian free field on the cable system of a transient weighted graph with volume growth exponent and Green function decay exponent . We…
Fractal dimension of critical Gaussian free field sign clusters
Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
We study metric graph sign clusters of the Gaussian free field on a large class of transient weighted graphs that are sufficiently low-dimensional, i.e. below the mean-field re…
Arm exponent for the Gaussian free field on metric graphs in intermediate dimensions
Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
We investigate the bond percolation model on transient weighted graphs induced by the excursion sets of the Gaussian free field on the corresponding metric graph. We assume t…
The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature
Roland Bauerschmidt, Jiwoon Park, Pierre-François Rodriguez
The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions, at sufficiently high temperature, we show that the scaling limit…
Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension
Hugo Duminil-Copin, Alejandro Rivera, Pierre-François Rodriguez +1
For the Bargmann--Fock field on with , we prove that the critical level of the percolation model formed by the excursion sets is…
On the radius of Gaussian free field excursion clusters
Subhajit Goswami, Pierre-François Rodriguez, Franco Severo
We consider the Gaussian free field on , for , and give sharp bounds on the probability that the radius of a finite cluster in the excursion set $\{φ\geq…
Equality of critical parameters for percolation of Gaussian free field level-sets
Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez +1
We consider upper level-sets of the Gaussian free field on , for , above a given real-valued height parameter . As varies, this defines a canonical per…
Geometry of Gaussian free field sign clusters and random interlacements
Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
For a large class of amenable transient weighted graphs , we prove that the sign clusters of the Gaussian free field on fall into a regime of strong supercriticality, in whi…
Decoupling inequalities for the Ginzburg-Landau models
Pierre-François Rodriguez
We consider a class of of massless gradient Gibbs measures, in dimension greater or equal to three, and prove a decoupling inequality for these fields. As a result, we obtain detai…
Some Applications of the Lee-Yang Theorem
Jürg Fröhlich, Pierre-François Rodriguez
For lattice systems of statistical mechanics satisfying a Lee-Yang property (i.e., for which the Lee-Yang circle theorem holds), we present a simple proof of analyticity of (connec…