Welcome to my web page. Here, you will find a description of my past and current research (full list below), as well as pictures of mathematical objects and some notes on simulations.


I am a directeur de recherche at the math department of ENS Lyon (moving to the Institut Fourier in Grenoble in September), and a member of the probability team. My main research interest is in statistical physics, especially the study of critical phenomena in two dimensions. I spent most of the academic years 2013-2015 in Bonn, Germany (at the Max-Planck Institut and then the Hausdorff Center).

Images and simulations

During my PhD and since then, I produced quite a few pictures of various two- dimensional objects, especially of SLE processes. Some of them can be found here, and a few comments about the programs used to generate them are gathered here (I am planning to set up separate pages for a few of the programs, which will be linked from there as well).


  1. Beffara, Vincent, On conformally invariant subsets of the planar Brownian curve, Annales de l’Institut Henri Poincare (B) Probability and Statistics 39 (2003), 793–821. [PDF] [link]
  2. Beffara, Vincent, Hausdorff dimensions for SLE6, The Annals of Probability 32 (2004), 2606–2629. [PDF] [link]
  3. Beffara, Vincent and Sidoravicius, Vladas and Spohn, Herbert and Vares, M. E., Polymer pinning in a random medium as influence percolation, in Dynamics & Stochastics, vol. 48 of IMS Lecture Notes, Monograph Series, (2006), 1–15. [PDF] [link]
  4. Beffara, Vincent, Cardy’s formula on the triangular lattice, the easy way, in Universality and renormalization, vol. 50 of Fields Institute Communications, (2007), 1–8. [PDF] [link]
  5. Beffara, Vincent, Is critical 2D percolation universal?, in In and Out of Equilibrium 2, vol. 60 of Progress in Probability, (2008), 31–58. [PDF] [link]
  6. Beffara, Vincent, The dimension of the SLE curves, The Annals of Probability 36 (2008), 1421–1452. [PDF] [link]
  7. Beffara, Vincent, Grands graphes planaires aléatoires et carte brownienne, Astérisque 326 (2009), 299–320. [PDF] [link]
  8. Beffara, Vincent and Sidoravicius, Vladas and Vares, Maria Eulalia, Randomized polynuclear growth with a columnar defect, Probability Theory and Related Fields 147 (2010), 565–581. [PDF] [link]
  9. Beffara, Vincent and Friedli, Sacha and Velenik, Yvan, Scaling Limit of the Prudent Walk, Electronic Communications in Probability 15 (2010), 44–58. [PDF] [link]
  10. Beffara, Vincent and Nolin, Pierre, On monochromatic arm exponents for 2D critical percolation, The Annals of Probability 39 (2011), 1286–1304. [PDF] [link]
  11. Beffara, Vincent and Duminil-Copin, Hugo, Smirnov’s fermionic observable away from criticality, The Annals of Probability 40 (2012), 2667–2689. [PDF] [link]
  12. Beffara, Vincent and Duminil-Copin, Hugo, The self-dual point of the two-dimensional random-cluster model is critical for q ≥ 1, Probability Theory and Related Fields 153 (2012), 511–542. [PDF] [link]
  13. Bálint, András and Beffara, Vincent and Tassion, Vincent, Confidence intervals for the critical value in the divide and color model, ALEA 10 (2013), 667–679. [PDF]
  14. Beffara, Vincent and Duminil-Copin, Hugo, Planar percolation with a glimpse of Schramm–Loewner evolution, Probability Surveys 10 (2013), 1–50. [PDF] [link]
  15. Bálint, András and Beffara, Vincent and Tassion, Vincent, On the critical value function in the divide and color model, ALEA 10 (2013), 653–666. [PDF]
  16. Beffara, Vincent and Donati-Martin, Catherine and Rouault, Alain, Bridges and random truncations of random matrices, Random Matrices: Theory and Applications 03 (2014), 1450006. [PDF] [link]


  1. Beffara, Vincent, Critical percolation on mesoscopic triangulations, Preprint arXiv:1312.7159 (2014), 1–13. [PDF] [link]
  2. Beffara, Vincent and Duminil-Copin, Hugo and Smirnov, Stanislav, On the critical parameters of the q ≥ 4 random-cluster model on isoradial graphs, Preprint arXiv:1507.01356 (2015), 1–25. [PDF] [link]
  3. Beffara, Vincent, Dessins d’enfants for analysts, Preprint arXiv:1504.00244 (2015), 1–32. [PDF] [link]

Other documents

  1. Beffara, Vincent, Mouvement Brownien Plan, SLE, Invariance Conforme et Dimensions Fractales, PhD thesis, 2003. [PDF]
  2. Beffara, Vincent and Nolin, Pierre, Numerical estimates for monochromatic percolation exponents, Unpublished, 2009. [PDF]
  3. Beffara, Vincent, Mécanique statistique et criticalité en dimension deux, Habilitation thesis (HDR), 2011. [PDF]
  4. Beffara, Vincent, La percolation, et un résultat de S. Smirnov, Gazette des Mathématiciens 128 (2011), 5–14. [PDF]
  5. Beffara, Vincent, Schramm-Loewner Evolution and other conformally invariant objects, in Probability and Statistical Physics in Two and More Dimensions, vol. 15 of Clay Mathematics Proceedings, (2012), 1–48. [PDF]
  6. Beffara, Vincent and Duminil-copin, Hugo, Critical point and duality in planar lattice models, in Saint Petersburg School on Probability and Statistical Physics, vol. xxx of Proceedings of Symposia in Pure Mathematics, (2014), 1–51. [PDF]
  7. Beffara, Vincent, Raconte-moi ... le processus SLE, Gazette des Mathématiciens 144 (2015), 59–63. [PDF]