Professional web page of Hugo Vanneuville

Click here for the French version.

Introduction:

Hello! I am Hugo Vanneuville, I am a researcher in math. Since January 2021, I am a CNRS researcher at Institut Fourier (Université Grenoble Alpes) in the probability team. Before this, I have completed a PhD at Institut Camille Jordan (Université Lyon 1) under the direction of Christophe Garban and I have been a post-doctoral resarcher at the math department of ETH Zürich under the direction of Vincent Tassion.

I am mainly interested in the study of phase transition and noise sensitivity phenomenons in percolation models. You can find more information below.

Two things before math:

  • I have stoped writing reports for journals published by Springer or Elsevier a few years ago: there is no reason why commercial publishers should make huge profits based on works donated for free by researchers, and charge our libraries exorbitant prices.

  • About a manifesto (in French): Avec quelques collègues de Lyon et Grenoble, nous avons lancé un manifeste pour la limitation de l'avion dans les laboratoires de maths, déjà signé par plus de 600 collègues de laboratoires de maths en France, et qui a obtenu le soutien de la Société Mathématique de France (SMF), la Société de Mathématiques Appliquées et Industrielles (SMAI) et la Société Française de Statistique (SFdS). De tels changements de pratique sont aussi l’occasion enthousiasmante de réfléchir à de nouvelles formes de rencontres scientifiques !
    • Organisation of events:

    Seminars/Reading groups:

  • Inter-thematic seminar at Institut Fourier.
  • Probability seminar at Institut Fourier (programme from autumn 2021).
  • Reading group in Zürich on random nodal lines, autumn 2019.

    • Conferences:

  • (A conference in French for mathematicians who want to learn more about ecological issues.) Je suis dans le comité scientifique de la conférence Climathiques qui aura lieu du 13 au 17 janvier 2025 au CIRM : "Une semaine à destination des mathématicien.nes désirant s’approprier les enjeux écologiques".
  • PPPP 2023 : Superconcentration and chaos, the example of First Passage Percolation, from May 31th to June 2nd, 2023 at Institut Fourier.
  • Lyon-Grenoble-Geneva Probability Day, November 17th, 2022 at Institut Fourier.

    • Research interests:

    I am interested in phase transition and noise sensitivity phenomenons in percolation models and in the universality properties of these models (in 2D in most of my works). In percolation theory, one studies the connectivity properties of random sets (such as a random subset of edges of a given lattice, or level sets of a random function). When the density of the random set reaches some critical value, fractal structures appear; they are the sign of the emergence of interactions at all scales.

    More specifically, the following three questions are guiding my research (among others):
  • Can we find new ways of formalising the fact that a threshold effect appears if the event that we study "depends little on every given coordinate"?
  • How can we show noise sensitivity properties without using any spectral tool?
  • Can we prove universality properties by using noise sensitivity?

    • (See also here for an interview done by INSMI when I was recruited, in which I describe my field of research - in French).

    Photo
    Figures: Percolation on a random tiling: each face is colored black with probability p=0.4, 0.5 and 0.6 respectively. In red: the points connected to the left side by a black path. There is a transition at p=0.5.
    Research papers:

    About the phase transition in Bernoulli percolation:

  • Exponential decay of the volume for Bernoulli percolation: a proof via stochastic comparison     (preprint)

    • New approaches to noise sensitivity:

  • Noise sensitivity of percolation via differential inequalities     with Vincent Tassion   (Proceedings of the London Mathematical Society, 2023)

    • Random nodal lines:

  • Existence of an unbounded nodal hypersurface for smooth Gaussian fields in dimension d >= 3     with Hugo Duminil-Copin, Alejandro Rivera and Pierre-François Rodriguez   (Annals of Probability, 2023 ; the published version contains one error, see the erratum. This error has been corrected in the arXiv version.)
  • The phase transition for planar Gaussian percolation models without FKG     with Stephen Muirhead and Alejandro Rivera, and with an appendix written by Laurin Köhler-Schindler   (Annals of Probability, 2023)
  • Bargmann-Fock percolation is noise sensitive     with Christophe Garban   (Electronic Journal of Probability, 2020)
  • The sharp phase transition for level set percolation of smooth planar Gaussian fields     with Stephen Muirhead   (Annales de l'Institut Henri Poincaré, prob. et stat., 2020)
  • The critical threshold for Bargmann-Fock percolation     with Alejandro Rivera   (Annales Henri Lebesgue, 2020)
  • Quasi-independence for nodal lines     with Alejandro Rivera   (Annales de l'Institut Henri Poincaré, prob. et stat., 2019)

    • Voronoi percolation, noise sensitivity and dynamics:

  • The annealed spectral sample of Voronoi percolation     (Annals of Probability, 2021)
  • Quantitative quenched Voronoi percolation and applications     (Annales de l'Institut Fourier, to appear)
  • Annealed scaling relations for Voronoi percolation     (Electronic Journal of Probability, 2019)
  • Exceptional times for percolation under exclusion dynamics     with Christophe Garban   (Annales scientifiques de l'École Normale Supérieure, 2019)

    • Other writings (not for publication):

  • Sharpness of Bernoulli percolation via couplings
  • Overview and concentration results for nodal lines     (introductory text for the reading group on random nodal lines organized at Zürich in 2019)
  • Percolation in the plane: dynamics, random tilings and nodal lines     (PhD thesis under the direction of Christophe Garban -- the introduction is written in French and the chapters are written in English)     Slides   Small erratum

    • List of my co-authors:

    Hugo Duminil-Copin, Christophe Garban, Laurin Köhler-Schindler, Stephen Muirhead, Alejandro Rivera, Pierre-François Rodriguez, Vincent Tassion

    Teaching:

    I taught at Université Lyon 1 during my PhD thesis. At Université Grenoble Alpes, I taught the course "Random models on lattices" with Loren Coquille during the first semester of the year 2023-2024. You can find the course summary here. During the second semester of the years 2021-2022, 2022-2023 and 2023-2024, I taught with Agnès Coquio the M1 course "Markov processes".

    Videos at Percolation Today:

  • Sharpness of Bernoulli percolation via couplings
  • Existence of an unbounded nodal surface for 3D smooth Gaussian fields
  • Noise sensitivity of percolation via differential inequalities (with Vincent Tassion)
  • The phase transition for planar Gaussian percolation without FKG (with Stephen Muirhead)

    • A counterexample?

    Consider the hypercube {0,1}^n equipped with the product probability measures of parameter p, that we denote by P_p. Let A be an increasing subset of {0,1}^n. Thanks to the works of Russo, BKKKL and Talagrand, we know if max_{i,p} P_p [changing the i^th coordinate changes 1_A] is small, then A satisfies a sharp threshold in the sense that P_p[A] is either close to 0 or close to 1 except when p belongs to some small interval. Now, let q such that P_q[A]=1/2. Is it still true if we only assume that max_i P_q [changing the i^th coordinate changes 1_A] is small?

    Diffusion (in French):

    J'ai fait un exposé lors du "Barcamp" organisé par les bibliothécaires de Lyon 1 en mai 2018. Vous pouvez trouver la vidéo ici.