Vincent Beffara

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 too).



V. Beffara. On conformally invariant subsets of the planar Brownian curve. Annales de l’Institut Henri Poincare (B) Probability and Statistics, 39(5):793–821, May 2001. URL: http://linkinghub.elsevier.com/retrieve/pii/S024602030300030X, doi:10.1016/S0246-0203(03)00030-X.


V. Beffara. Hausdorff dimensions for SLE6. The Annals of Probability, 32(3B):2606–2629, July 2004. URL: http://projecteuclid.org/Dienst/getRecord?id=euclid.aop/1091813625/, doi:10.1214/009117904000000072.


V. Beffara. Cardy’s formula on the triangular lattice, the easy way. In I. Binder and D. Kreimer, editors, Universality and Renormalization, volume 50 of Fields Institute Communications, 1–8. The Fields Institute, 2007. URL: http://www.ams.org/bookstore-getitem/item=FIC-50.


V. Beffara. Is Critical 2D Percolation Universal? In In and Out of Equilibrium 2, volume 60 of Progress in Probability, pages 31–58. Birkhäuser Basel, Basel, 2008. URL: http://www.springerlink.com/index/10.1007/978-3-7643-8786-0_3, doi:10.1007/978-3-7643-8786-0_3.


V. Beffara. The dimension of the SLE curves. The Annals of Probability, 36(4):1421–1452, July 2008. URL: http://projecteuclid.org/euclid.aop/1217360974, doi:10.1214/07-AOP364.


V. Beffara. Grands graphes planaires aléatoires et carte brownienne. Astérisque, 326:299–320, 2009. URL: http://smf4.emath.fr/Publications/Asterisque/2009/326/html/smf_ast_326_299-320.php.


V. Beffara, S. Chhita and K. Johansson. Airy point process at the liquid-gas boundary. The Annals of Probability, 46(5):2973–3013, September 2018. URL: https://projecteuclid.org/euclid.aop/1535097644, doi:10.1214/17-AOP1244.


V. Beffara and H. Duminil-Copin. The self-dual point of the two-dimensional random-cluster model is critical for $q\geq 1$. Probability Theory and Related Fields, 153(3-4):511–542, August 2012. URL: http://link.springer.com/10.1007/s00440-011-0353-8, doi:10.1007/s00440-011-0353-8.


V. Beffara, H. Duminil-Copin and S. Smirnov. On the critical parameters of the $q\geq 4$ random-cluster model on isoradial graphs. Journal of Physics A: Mathematical and Theoretical, 48(48):484003, December 2015. URL: http://iopscience.iop.org/article/10.1088/1751-8113/48/48/484003/meta, doi:10.1088/1751-8113/48/48/484003.


V. Beffara, S. Friedli and Y. Velenik. Scaling Limit of the Prudent Walk. Electronic Communications in Probability, 15:44–58, February 2010. URL: http://projecteuclid.org/euclid.ecp/1465243948, doi:10.1214/ECP.v15-1527.


V. Beffara and D. Gayet. Percolation of random nodal lines. Publications mathématiques de l’IHÉS, 126(1):131–176, November 2017. URL: http://link.springer.com/10.1007/s10240-017-0093-0, doi:10.1007/s10240-017-0093-0.


V. Beffara and P. Nolin. On monochromatic arm exponents for 2D critical percolation. The Annals of Probability, 39(4):1286–1304, July 2011. URL: http://projecteuclid.org/euclid.aop/1312555798, doi:10.1214/10-AOP581.


V. Beffara, V. Sidoravicius, H. Spohn and M. E. Vares. Polymer pinning in a random medium as influence percolation. IMS Lecture Notes, Monograph Series, 48:1–15, 2006. URL: http://projecteuclid.org/euclid.lnms/1196285803, doi:10.1214/074921706000000022.


V. Beffara, V. Sidoravicius and M. E. Vares. Randomized polynuclear growth with a columnar defect. Probability Theory and Related Fields, 147(3):565–581, April 2010. URL: http://link.springer.com/10.1007/s00440-009-0216-8, doi:10.1007/s00440-009-0216-8.


V. Beffara, C. Donati-Martin and A. Rouault. Bridges and random truncations of random matrices. Random Matrices: Theory and Applications, 03(02):1450006, May 2014. URL: http://www.worldscientific.com/doi/abs/10.1142/S2010326314500063, doi:10.1142/S2010326314500063.


V. Beffara and H. Duminil-Copin. Smirnov’s fermionic observable away from criticality. The Annals of Probability, 40(6):2667–2689, November 2012. URL: http://projecteuclid.org/euclid.aop/1351258736, doi:10.1214/11-AOP689.


V. Beffara and H. Duminil-Copin. Planar percolation with a glimpse of Schramm–Loewner evolution. Probability Surveys, 10:1–50, 2013. URL: http://www.i-journals.org/ps/viewarticle.php?id=186\&layout=abstract, doi:10.1214/11-PS186.


A. Bálint, V. Beffara and V. Tassion. Confidence intervals for the critical value in the divide and color model. Alea, 10(2):667–679, 2013.


A. Bálint, V. Beffara and V. Tassion. On the critical value function in the divide and color model. ALEA, 10(2):653–666, 2013. URL: http://arxiv.org/abs/1109.3403.



V. Beffara. Dessins d’enfants for analysts. preprint arXiv 1504.00244, pages 1–32, 2015. URL: http://arxiv.org/abs/1504.00244.


V. Beffara and D. Gayet. Percolation without FKG. preprint arXiv 1710.10644, pages 1–32, October 2017. URL: http://arxiv.org/abs/1710.10644.


V. Beffara and C. B. Huynh. Trees of self-avoiding walks. preprint arXiv 1711.05527, pages 1–39, November 2017. URL: https://arxiv.org/abs/1711.05527.


V. Beffara, C. B. Huynh and B. Lévêque. Scaling limits for random triangulations on the torus. arXiv:1905.01873 [cs, math], May 2019. URL: http://arxiv.org/abs/1905.01873, arXiv:1905.01873.


V. Beffara, E. Peltola and H. Wu. On the Uniqueness of Global Multiple SLEs. preprint arXiv 1801.07699, pages 1–30, January 2018. URL: http://arxiv.org/abs/1801.07699.

Other documents


V. Beffara. Mouvement Brownien Plan, SLE, Invariance Conforme et Dimensions Fractales. PhD thesis, Université Paris-Sud (Orsay), France, 2003.


V. Beffara. La percolation, et un résultat de S. Smirnov. Gazette des Mathématiciens, 128:5–14, 2011.


V. Beffara. Mécanique Statistique et Criticalité En Dimension Deux. PhD thesis, École Normale Supérieure de Lyon, France, 2011.


V. Beffara. Schramm-Loewner Evolution and other conformally invariant objects. In Probability and Statistical Physics in Two and More Dimensions, volume 15 of Clay Mathematics Proceedings, 1–48. AMS and the Clay Mathematics Institute, 2012.


V. Beffara. Raconte-moi … le processus SLE. Gazette des Mathématiciens, 144:59–63, 2015.


V. Beffara and H. Duminil-copin. Critical point and duality in planar lattice models. In Saint Petersburg School on Probability and Statistical Physics, volume xxx of Proceedings of Symposia in Pure Mathematics, 1–51. 2014.