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 Reader 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)
Events:
CUWB Probability-on-Sea Jan 8-12, 2024, Minicourse. Lecture notes.
Conference Herrsching am Ammersee, Germany, May 20-24, 2024. Webpage.
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Sharp threshold for the ballisticity of the random walk on the exclusion process
Preprint, 69 pages (2024).
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Critical one-arm probability for the metric Gaussian free field in low dimensions
Preprint, 17 pages (2024).
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Universality classes for percolation models with long-range correlations
Preprint, 6 pages (2024).
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Arm exponent for the Gaussian free field on metric graphs in intermediate dimensions
Preprint, 21 pages (2023).
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Phase transition for the late points of random walk
Preprint, 68 pages (2023); with a supplement here.
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Phase transition for the vacant set of random walk and random interlacements
Preprint, 94 pages (2023).
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A characterization of strong percolation via disconnection
Preprint, 46 pages (2023).
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Finite range interlacements and couplings
Preprint, 67 pages (2023).
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An isomorphism theorem for Ginzburg-Landau interface models and scaling limits
Probab. Theory Rel. Fields (to appear), 38 pages (2022).
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The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature
Ann. Probab. (to appear), 35 pages (2022).
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The Discrete Gaussian model, I. Renormalisation group flow at high temperature
Ann. Probab. (to appear), 93 pages (2022).
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Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension \(d\geqslant3\)
Ann. Probab. 51 (1), 228-276 (2023).
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Critical exponents for a percolation model on transient graphs
Invent. Math. 232 (1), 229-299 (2023).
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Cluster capacity functionals and isomorphism theorems for Gaussian free fields
Probab. Theory Rel. Fields 183, 255-313 (2022).
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On the radius of Gaussian free field excursion clusters.
Ann. Probab. 50 (5), 1675-1724 (2022).
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Equality of critical parameters for percolation of Gaussian free field level-sets
Duke Math. J. 172 (5), 839-913 (2023).
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Geometry of Gaussian free field sign clusters and random interlacements
Probab. Theory Rel. Fields (to appear), 78 pages (2018).
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The sign clusters of the massless free field percolate on \(\mathbb{Z}^d\), \(d\geqslant3\) (and more)
Commun. Math. Phys. 362 (2), 513-546 (2018).
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On pinned fields, interlacements, and random walk on \((\mathbb{Z}/N\mathbb{Z})^2\)
Probab. Theory Rel. Fields, 173, pp. 1265-1299 (2019).
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Limit theory for random walks in degenerate time-dependent random environments
J. Funct. Anal., 274 (4), pp. 985-1046 (2018).
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Decoupling inequalities for the Ginzburg-Landau \(\nabla \phi\) models
Preprint, submitted, 34 pages (2016).
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On cluster properties of classical ferromagnets in an external magnetic field
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).
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A 0-1 law for the massive Gaussian free field
Probab. Theory Rel. Fields, 169 (3-4), pp. 901-930 (2016).
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High-dimensional asymptotics for percolation of Gaussian free field level sets
Electron. J. Probab. 20 (47), pp. 1-39 (2015).
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Level set percolation for random interlacements and the Gaussian free field
Stoch. Proc. Appl. 124 (4), pp. 1469-1502 (2014).
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Phase transition and level set percolation for the Gaussian free field
Commun. Math. Phys. 320 (2), pp. 571-601 (2013).
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Some applications of the Lee-Yang theorem
J. Math. Phys. 53, 095218, pp. 1-15 (2012).
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Short bio
Before joining Imperial, I was working at IHÉS (Sept. 2018 to Feb. 2020), in the group 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, and grew up mostly in Germany.
A brief CV is available here.
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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.
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Percolation of sign clusters for the Gaussian free field I
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Percolation of sign clusters for the Gaussian free field II
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MATH 275 C - Spring 2017 The probabilistic construction of continuous-time Markov chains.
Related documents
Syllabus Homework 1 Homework 2 Homework 3