Pierre-François Rodriguez

Department of Mathematics, Imperial College London
South Kensington Campus
London SW7 2AZ
United Kingdom

email: p.rodriguez@imperial.ac.uk
office: 656, Huxley Building

Welcome to my homepage.

I am currently Lecturer (Assistant Professor) in Pure Mathematics at the Department of Mathematics of Imperial College London .

My main research interests are probability theory and mathematical physics, with a special focus on problems concerning phase transitions and random media.

Seminars:

To see the programme of our stochastic analysis seminar, click here .

I am also co-organizing the London analysis and probability seminar .

PhD Students:

Current: Yuriy Shulzhenko, Wen Zhang

Former: Alexis Prévost (joint with A. Drewitz)

Phase transition for the late points of random walk
A. Prévost, P.-F. Rodriguez, and P. Sousi.
Preprint, 68 pages (2023); with a supplement here .

Phase transition for the vacant set of random walk and random interlacements
H. Duminil-Copin, S. Goswami, P.-F. Rodriguez, F. Severo and A. Teixeira.
Preprint, 94 pages (2023).
A characterization of strong percolation via disconnection
H. Duminil-Copin, S. Goswami, P.-F. Rodriguez, F. Severo and A. Teixeira.
Preprint, 46 pages (2023).
Finite range interlacements and couplings
H. Duminil-Copin, S. Goswami, P.-F. Rodriguez, F. Severo and A. Teixeira.
Preprint, 67 pages (2023).
An isomorphism theorem for Ginzburg-Landau interface models and scaling limits
J.-D. Deuschel and P.-F. Rodriguez.
Preprint, 38 pages (2022).
The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature
R. Bauerschmidt, J. Park and P.-F. Rodriguez.
Ann. Probab. (to appear), 35 pages (2022).
The Discrete Gaussian model, I. Renormalisation group flow at high temperature
R. Bauerschmidt, J. Park and P.-F. Rodriguez.
Ann. Probab. (to appear), 93 pages (2022).
Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension \(d\geqslant3\)
H. Duminil-Copin, A. Rivera, P.-F. Rodriguez and H. Vanneuville.
Ann. Probab. 51 (1), 228-276 (2023).
Critical exponents for a percolation model on transient graphs
A. Drewitz, A. Prévost and P.-F. Rodriguez.
Invent. Math. 232 (1), 229-299 (2023).
Cluster capacity functionals and isomorphism theorems for Gaussian free fields
A. Drewitz, A. Prévost and P.-F. Rodriguez.
Probab. Theory Rel. Fields 183, 255-313 (2022).
On the radius of Gaussian free field excursion clusters.
S. Goswami, P.-F. Rodriguez and F. Severo.
Ann. Probab. 50 (5), 1675-1724 (2022).
Equality of critical parameters for percolation of Gaussian free field level-sets
H. Duminil-Copin, S. Goswami, P.-F. Rodriguez and F. Severo.
Duke Math. J. (to appear), 54 pages (2020).
Geometry of Gaussian free field sign clusters and random interlacements
A. Drewitz, A. Prévost and P.-F. Rodriguez.
Preprint, 78 pages (2018).
The sign clusters of the massless free field percolate on \(\mathbb{Z}^d\), \(d\geqslant3\) (and more)
A. Drewitz, A. Prévost and P.-F. Rodriguez.
Commun. Math. Phys. 362 (2), 513-546 (2018).
On pinned fields, interlacements, and random walk on \((\mathbb{Z}/N\mathbb{Z})^2\)
P.-F. Rodriguez.
Probab. Theory Rel. Fields, 173, pp. 1265-1299 (2019).
Limit theory for random walks in degenerate time-dependent random environments
M. Biskup and P.-F. Rodriguez.
J. Funct. Anal., 274 (4), pp. 985-1046 (2018).
Decoupling inequalities for the Ginzburg-Landau \(\nabla \phi\) models
P.-F. Rodriguez.
Preprint, submitted, 34 pages (2016).
On cluster properties of classical ferromagnets in an external magnetic field
J. Fröhlich and P.-F. Rodriguez.
J. Stat. Phys. 166 (3-4), pp. 828-840 (Special issue on the occasion of David Ruelle's and Yakov Sinai's 80'th birthdays), (2017).
A 0-1 law for the massive Gaussian free field
P.-F. Rodriguez.
Probab. Theory Rel. Fields, 169 (3-4), pp. 901-930 (2016).
High-dimensional asymptotics for percolation of Gaussian free field level sets
A. Drewitz and P.-F.Rodriguez.
Electron. J. Probab. 20 (47), pp. 1-39 (2015).
Level set percolation for random interlacements and the Gaussian free field
P.-F. Rodriguez.
Stoch. Proc. Appl. 124 (4), pp. 1469-1502 (2014).
Phase transition and level set percolation for the Gaussian free field
P.-F. Rodriguez and A.-S. Sznitman.
Commun. Math. Phys. 320 (2), pp. 571-601 (2013).
Some applications of the Lee-Yang theorem
J. Fröhlich and P.-F. Rodriguez.
J. Math. Phys. 53, 095218, pp. 1-15 (2012).

Short bio
Before joining Imperial, I was working at IHÉS (Sept. 2018 to Feb. 2020), where my research was supported by the ERC Grant CriBLaM of Hugo Duminil-Copin. Prior to IHÉS, I held a position as E.R. Hedrick Assistant Professor at the Department of Mathematics, UCLA. My host was Marek Biskup.

I received a Ph.D. in Mathematics from ETH Zurich, under the guidance of Alain-Sol Sznitman.

I have French and Spanish origins. I grew up mostly in Germany.

A more detailed CV is available here.

Below are the recordings of two talks I gave at the Institute for Advanced Study about my work with Alexander Drewitz and Alexis Prévost. The corresponding article is available here.
Percolation of sign clusters for the Gaussian free field I
Percolation of sign clusters for the Gaussian free field II

MATH 50006 Lebesgue Measure and Integration All information/content related to this module will be made available through Blackboard. Lecture notes are also available here: Chapter 1 , Chapter 2 , Chapter 3 , Chapter 4 (this version: 14/03/2021).

MATH 275 C - Spring 2017 The probabilistic construction of continuous-time Markov chains.
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Syllabus Homework 1 Homework 2 Homework 3

Pierre-François Rodriguez

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