Pierre-François Rodriguez

Professor of Mathematics

DPMMS, Center for Mathematical Sciences / University of Cambridge
Email: pfr26 [at] cam [dot] ac [dot] uk

Mailing address:
University of Cambridge
Wilberforce Road
Cambridge CB3 0WB
United Kingdom

arXiv · ORCID

I am a researcher in pure mathematics with interests in probability theory, and related fields. The questions I like to think about often have links with (mathematical) physics. Most of my work focuses on problems involving critical phenomena.

Bio

I moved to Cambridge in Summer 2025.

I am also Visiting Professor at Imperial College London, where I advise Wen Zhang.

A brief CV is available here.

Research

Some recent events

  • Random Walks, Percolation and Mixing Time
    9-13 June 2025, ICMS, Edinburgh
    Org. with Daniel Kious, Bruno Schapira and Perla Sousi. Webpage.
  • Geometry of Random Fields and Random Walk Clusters: New Horizons
    Oberwolfach Mini-Workshop, Germany, Dec 8-13, 2024
    Org. with Titus Lupu and Wei Qian. Report.
  • Random Walks, Scaling Limits and Criticality
    Herrsching am Ammersee, Germany, May 20-24, 2024.
    Org. with Noam Berger and Nina Gantert. Webpage.
  • CUWB Probability-on-Sea, Playa del Carmen, MEX, Jan 8-12, 2024
    Notes from a mini-course are available here.

Publications

Below are all my published articles and preprints, listed in reverse chronological order (by first appearance on arXiv).

  • [pdf] [arXiv] Anomalous scaling law for the two-dimensional Gaussian free field
    Pierre-François Rodriguez, Wen Zhang
    arXiv preprint (2025)
  • [pdf] [arXiv] On cable-graph percolation between dimensions 2 and 3
    Pierre-François Rodriguez, Wen Zhang
    arXiv preprint (2025)
  • [pdf] [arXiv] Arm exponent for the Gaussian free field on metric graphs in intermediate dimensions
    Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
    arXiv preprint (2023)
  • [pdf] [arXiv] Strong local uniqueness for the vacant set of random interlacements
    Subhajit Goswami, Pierre-François Rodriguez, Yuriy Shulzhenko
    arXiv preprint (2025)
  • [pdf] [arXiv] Sharp connectivity bounds for the vacant set of random interlacements
    Subhajit Goswami, Pierre-François Rodriguez, Yuriy Shulzhenko
    arXiv preprint (2025)
  • [pdf] [arXiv] Cluster volumes for the Gaussian free field on metric graphs
    Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
    arXiv preprint (2024)
  • [pdf] [arXiv] Sharp threshold for the ballisticity of the random walk on the exclusion process
    Guillaume Conchon-Kerjan, Daniel Kious, Pierre-François Rodriguez
    arXiv preprint (2024)
  • [pdf] [arXiv] Equality of critical parameters for percolation of Gaussian free field level-sets
    Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez, Franco Severo
    Duke Mathematical Journal 172 (2023), no. 5, 839–913
  • [pdf] [arXiv] Critical one-arm probability for the metric Gaussian free field in low dimensions
    Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
    arXiv preprint (2024)
  • [pdf] [arXiv] Geometry of Gaussian free field sign clusters and random interlacements
    Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
    Probability Theory and Related Fields 192, 625–720 (2025)
  • [pdf] [arXiv] Universality classes for percolation models with long-range correlations
    Christopher Chalhoub, Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
    arXiv preprint (2024)
  • [pdf] [arXiv] A Ray-Knight theorem for ∇φ interface models and scaling limits
    Jean-Dominique Deuschel, Pierre-François Rodriguez
    arXiv preprint (2022)
  • [pdf] [arXiv] Phase transition for the late points of random walk
    Alexis Prévost, Pierre-François Rodriguez, Perla Sousi
    arXiv preprint (2023)
  • [pdf] [arXiv] The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature
    Roland Bauerschmidt, Jiwoon Park, Pierre-François Rodriguez
    Annals of Probability 52, 1360–1398 (2024)
  • [pdf] [arXiv] The Discrete Gaussian model, I. Renormalisation group flow at high temperature
    Roland Bauerschmidt, Jiwoon Park, Pierre-François Rodriguez
    Annals of Probability 52, 1253–1359 (2024)
  • [pdf] [arXiv] A characterization of strong percolation via disconnection
    Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez, Franco Severo, Augusto Teixeira
    arXiv preprint (2023)
  • [pdf] [arXiv] Phase transition for the vacant set of random walk and random interlacements
    Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez, Franco Severo, Augusto Teixeira
    arXiv preprint (2023)
  • [pdf] [arXiv] Finite range interlacements and couplings
    Hugo Duminil-Copin, Subhajit Goswami, Pierre-François Rodriguez, Franco Severo, Augusto Teixeira
    arXiv preprint (2023)
  • [pdf] [arXiv] Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d ≥ 3
    Hugo Duminil-Copin, Alejandro Rivera, Pierre-François Rodriguez, Hugo Vanneuville
    arXiv preprint (2021)
  • [pdf] [arXiv] Critical exponents for a percolation model on transient graphs
    Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
    Inventiones Mathematicae 232, 229–299 (2023)
  • [pdf] [arXiv] On the radius of Gaussian free field excursion clusters
    Subhajit Goswami, Pierre-François Rodriguez, Franco Severo
    Annals of Probability 50(5):1675–1724 (2022)
  • [pdf] [arXiv] Cluster capacity functionals and isomorphism theorems for Gaussian free fields
    Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
    Probability Theory and Related Fields 183(1-2):255–313 (2022)
  • [pdf] [arXiv] The sign clusters of the massless Gaussian free field percolate on ℤᵈ, d ≥ 3
    Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
    Communications in Mathematical Physics 362, 513–546 (2018)
  • [pdf] [arXiv] Limit theory for random walks in degenerate time-dependent random environments
    Marek Biskup, Pierre-François Rodriguez
    Journal of Functional Analysis 274(4):985–1046 (2018)
  • [pdf] [arXiv] On cluster properties of classical ferromagnets in an external magnetic field
    Jürg Fröhlich, Pierre-François Rodriguez
    Journal of Statistical Physics 166(3-4), 828–840 (2017)
  • [pdf] [arXiv] A 0-1 law for the Gaussian free field
    Pierre-François Rodriguez
    Probab. Theory Rel. Fields, Vol. 169, pp. 901-930 (2016).
  • [pdf] [arXiv] High-dimensional asymptotics for percolation of Gaussian free field level sets
    Alexander Drewitz, Pierre-François Rodriguez
    Electr. J. Prob., Vol. 20, pp. 1–39 (2015)
  • [pdf] [arXiv] Level set percolation for random interlacements and the Gaussian free field
    Pierre-François Rodriguez
    Stoch. Proc. Appl. (SPA), Vol. 124, pp. 1469–1502 (2014)
  • [pdf] [arXiv] Phase transition and level-set percolation for the Gaussian free field
    Pierre-François Rodriguez, Alain-Sol Sznitman
    Comm. Math. Phys., Vol. 320, pp. 571–601 (2013)
  • [pdf] [arXiv] Some applications of the Lee-Yang theorem
    Jürg Fröhlich, Pierre-François Rodriguez
    J. Math. Phys., Vol. 53, pp. 1–15 (2012)

A complete and up-to-date list of publications can also be found on my arXiv author page.

Teaching

In Lent 26 I will be teaching a Part III course entitled "Random Walks and Critical Phenomena". A brief course outline, including prerequisites, is available here.

From past courses:

  • Lebesgue Measure and Integration
    The lecture notes for MATH 50006 (@Imperial) are still available here.
  • Stochastic Processes
    The probabilistic construction of continuous-time Markov chains (from MATH 275C, a graduate course @UCLA).