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. V. Beffara, S. Chhita and K. Johansson, “Airy point process at the liquid-gas boundary”, The Annals of Probability, vol. 46, no. 5, 2973–3013, Sep. 2018. [PDF] [link] [slides]
  2. V. Beffara and D. Gayet, “Percolation of random nodal lines”, Publications mathématiques de l’IHÉS, vol. 126, no. 1, 131–176, Nov. 2017. [PDF] [link]
  3. V. Beffara, H. Duminil-Copin and S. Smirnov, “On the critical parameters of the q\ge4 random-cluster model on isoradial graphs”, Journal of Physics A: Mathematical and Theoretical, vol. 48, no. 48, 484003, Dec. 2015. [PDF] [link]
  4. V. Beffara, C. Donati-Martin and A. Rouault, “Bridges and random truncations of random matrices”, Random Matrices: Theory and Applications, vol. 3, no. 2, 1450006, May 2014. [PDF] [link]
  5. V. Beffara and H. Duminil-Copin, “Planar percolation with a glimpse of Schramm–Loewner evolution”, Probability Surveys, vol. 10, 1–50, 2013. [PDF] [link]
  6. A. Bálint, V. Beffara and V. Tassion, “Confidence intervals for the critical value in the divide and color model”, Alea, vol. 10, no. 2, 667–679, 2013. [PDF]
  7. V. Beffara and H. Duminil-Copin, “Smirnov’s fermionic observable away from criticality”, The Annals of Probability, vol. 40, no. 6, 2667–2689, Nov. 2012. [PDF] [link]
  8. V. Beffara and H. Duminil-Copin, “The self-dual point of the two-dimensional random-cluster model is critical for q\ge1”, Probability Theory and Related Fields, vol. 153, no. 3, 511–542, Aug. 2012. [PDF] [link]
  9. A. Bálint, V. Beffara and V. Tassion, “On the critical value function in the divide and color model”, ALEA, vol. 10, no. 2, 653–666, Sep. 2011. [PDF] [link]
  10. V. Beffara and P. Nolin, “On monochromatic arm exponents for 2D critical percolation”, The Annals of Probability, vol. 39, no. 4, 1286–1304, Jul. 2011. [PDF] [link]
  11. V. Beffara, V. Sidoravicius and M. E. Vares, “Randomized polynuclear growth with a columnar defect”, Probability Theory and Related Fields, vol. 147, no. 3, 565–581, Apr. 2010. [PDF] [link]
  12. V. Beffara, S. Friedli and Y. Velenik, “Scaling Limit of the Prudent Walk”, Electronic Communications in Probability, vol. 15, 44–58, Feb. 2010. [PDF] [link]
  13. V. Beffara, “Grands graphes planaires aléatoires et carte brownienne”, Astérisque, vol. 326, 299–320, 2009. [PDF] [link]
  14. V. Beffara, “The dimension of the SLE curves”, The Annals of Probability, vol. 36, no. 4, 1421–1452, Jul. 2008. [PDF] [link]
  15. V. Beffara, “Is Critical 2D Percolation Universal?”, in In and Out of Equilibrium 2, vol. 60, Basel: Birkhäuser Basel, 2008, 31–58. [PDF] [link]
  16. V. Beffara, “Cardy’s formula on the triangular lattice, the easy way”, in Universality and renormalization, 2007, vol. 50, 1–8. [PDF] [link]
  17. V. Beffara, V. Sidoravicius, H. Spohn and M. E. Vares, “Polymer pinning in a random medium as influence percolation”, IMS Lecture Notes, Monograph Series, vol. 48, 1–15, 2006. [PDF] [link]
  18. V. Beffara, “Hausdorff dimensions for SLE6”, The Annals of Probability, vol. 32, no. 3, 2606–2629, Jul. 2004. [PDF] [link]
  19. V. Beffara, “On conformally invariant subsets of the planar Brownian curve”, Annales de l’Institut Henri Poincare (B) Probability and Statistics, vol. 39, no. 5, 793–821, May 2001. [PDF] [link]


  1. V. Beffara, E. Peltola and H. Wu, “On the Uniqueness of Global Multiple SLEs”, Preprint, 1–30, Jan. 2018. [PDF] [link]
  2. V. Beffara and C. B. Huynh, “Trees of self-avoiding walks”, Preprint, 1–39, Nov. 2017. [PDF] [link]
  3. V. Beffara and D. Gayet, “Percolation without FKG”, Preprint, 1–32, Oct. 2017. [PDF] [link]
  4. V. Beffara, “Dessins d’enfants for analysts”, Preprint, 1–32, 2015. [PDF] [link]

Other documents

  1. V. Beffara, “Raconte-moi … le processus SLE”, Gazette des Mathématiciens, vol. 144, 59–63, 2015. [PDF]
  2. V. Beffara and H. Duminil-copin, “Critical point and duality in planar lattice models”, in Saint Petersburg School on Probability and Statistical Physics, 2014, vol. xxx, 1–51. [PDF]
  3. V. Beffara, “Schramm-Loewner Evolution and other conformally invariant objects”, in Probability and Statistical Physics in Two and More Dimensions, 2012, vol. 15, 1–48. [PDF]
  4. V. Beffara, “Mécanique statistique et criticalité en dimension deux”, Habilitation thesis, École Normale Supérieure de Lyon, France, 2011. [PDF]
  5. V. Beffara, “La percolation, et un résultat de S. Smirnov”, Gazette des Mathématiciens, vol. 128, 5–14, 2011. [PDF]
  6. V. Beffara, “Mouvement Brownien Plan, SLE, Invariance Conforme et Dimensions Fractales”, PhD thesis, Université Paris-Sud (Orsay), France, 2003. [PDF]