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 Institut Fourier in Grenoble, 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), and was previously at the École Normale Supérieure in Lyon.

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 and Duminil-Copin, Hugo and Smirnov, Stanislav, On the critical parameters of the q\ge4 random-cluster model on isoradial graphs, Journal of Physics A: Mathematical and Theoretical 48 (2015), 484003. (BDS:largeq) [link]
  2. 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]
  3. 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]
  4. 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]
  5. Beffara, Vincent and Duminil-Copin, Hugo, Planar percolation with a glimpse of Schramm–Loewner evolution, Probability Surveys 10 (2013), 1–50. [PDF] [link]
  6. Beffara, Vincent and Duminil-Copin, Hugo, Smirnov’s fermionic observable away from criticality, The Annals of Probability 40 (2012), 2667–2689. [PDF] [link]
  7. Beffara, Vincent and Duminil-Copin, Hugo, The self-dual point of the two-dimensional random-cluster model is critical for q\ge1, Probability Theory and Related Fields 153 (2012), 511–542. [PDF] [link]
  8. Beffara, Vincent and Nolin, Pierre, On monochromatic arm exponents for 2D critical percolation, The Annals of Probability 39 (2011), 1286–1304. [PDF] [link]
  9. 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. (BSV:rpng) [link]
  10. Beffara, Vincent and Friedli, Sacha and Velenik, Yvan, Scaling Limit of the Prudent Walk, Electronic Communications in Probability 15 (2010), 44–58. [PDF] [link]
  11. Beffara, Vincent, Grands graphes planaires aléatoires et carte brownienne, Astérisque 326 (2009), 299–320. [PDF] [link]
  12. 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]
  13. Beffara, Vincent, The dimension of the SLE curves, The Annals of Probability 36 (2008), 1421–1452. [PDF] [link]
  14. 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]
  15. Beffara, Vincent and Sidoravicius, Vladas and Spohn, Herbert and Vares, M. E., Polymer pinning in a random medium as influence percolation, in Dynamics and Stochastics, vol. 48 of IMS Lecture Notes, Monograph Series, (2006), 1–15. [PDF] [link]
  16. Beffara, Vincent, Hausdorff dimensions for SLE6, The Annals of Probability 32 (2004), 2606–2629. [PDF] [link]
  17. 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]


  1. Beffara, Vincent, Dessins d’enfants for analysts, Preprint arXiv:1504.00244 (2015), 1–32. [PDF] [link]
  2. Beffara, Vincent, Critical percolation on mesoscopic triangulations, Preprint arXiv:1312.7159 (2014), 1–13. [PDF] [link]

Other documents

  1. Beffara, Vincent, Raconte-moi ... le processus SLE, Gazette des Mathématiciens 144 (2015), 59–63. [PDF]
  2. 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]
  3. 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]
  4. Beffara, Vincent, La percolation, et un résultat de S. Smirnov, Gazette des Mathématiciens 128 (2011), 5–14. [PDF]
  5. Beffara, Vincent, Mécanique statistique et criticalité en dimension deux, Habilitation thesis (HDR), 2011. [PDF]
  6. Beffara, Vincent and Nolin, Pierre, Numerical estimates for monochromatic percolation exponents, Unpublished, 2009. [PDF]
  7. Beffara, Vincent, Mouvement Brownien Plan, SLE, Invariance Conforme et Dimensions Fractales, PhD thesis, 2003. [PDF]