Research activities
  • Gaussian multiplicative chaos, multifractal random measures and their applications,
  • Liouville field theory and quantum gravity,
  • scaling limits, homogenization and invariance priciples,
  • random media,
Publication list
 

41-Liouville Quantum Gravity and Polyakov's formulation of 2d string theory with C.Guillarmou and V.Vargas.
40-Lecture notes on Gaussian multiplicative chaos and Liouville Quantum gravity with V.Vargas.
39-Conformal Ward and BPZ identities for Liouville quantum field teory with A.Kupiainen and V.Vargas.
38-Renormalizability of Liouville Quantum Gravity at the Seiberg bound, with F.David, A.Kupiainen and V.Vargas, 2015..
37-Liouville Quantum Gravity on the complex tori,  with F.David and V.Vargas, 2015.
36-Continuity estimates for the complex cascade model on the phase boundary,  with T. Madaule and V.Vargas, 2015.
35-Liouville quantum gravity on the unit disk,  with Y. Huang and V.Vargas, 2015.
34-Liouville quantum gravity on the Riemann sphere, with F.David, A.Kupiainen and V.Vargas, 2014.
33-Log-correlated Gaussian fields: an overview, with B.Duplantier, S.Sheffield and V.Vargas, 2014.
32-KPZ formula derived from Liouville heat kernel, with N.Berestycki, C.Garban and V.Vargas, 2014.
31-Liouville heat kernel: regularity and bounds, with P.Maillard, V.Vargas and O.Zeitouni, to appear in Annales de l'institut Henri Poincaré.
30-Large deviations for random surfaces: the hyperbolic nature of Liouville Field Theory, with H.Lacoin and V.Vargas, 2014.
29-Liouville Brownian motion at criticality, with V.Vargas, to appear in Potential Analysis.
28-The glassy phase of complex branching Brownian motion , with T.Madaule and V.Vargas, to appear in Commun. Math. Physics.
27-Glassy phase and freezing of log-correlated Gaussian potentials , with T.Madaule and V.Vargas, to appear in Annals of Applied Probability.
26-Complex Gaussian multiplicative chaos , with H.Lacoin and V.Vargas, to appear in Commun. Math. Physics.
25-Gaussian multiplicative chaos and applications: a review , with V.Vargas, to appear in Probability surveys.
24-Spectral dimension of Liouville quantum gravity , with V.Vargas, to appear in Annales Henri Poincaré.
23-On the heat kernel and the Dirichlet form of Liouville Brownian motion , with C.Garban and V.Vargas, to appear in Electron. Journal Probab.
22-Liouville Brownian motion , with C.Garban and V.Vargas, 2013, to appear in Annals of Probability.
21-Renormalization of critical Gaussian multiplicative chaos and KPZ formula , with B.Duplantier, S.Sheffield and V.Vargas, Commun. Math. Physics, 2014, Volume 330, Issue 1, pp 283-330.
20-Gaussian multiplicative chaos for symmetric isotropic matrices , with L.Chevillard and V.Vargas, Journal of Statistical Physics, February 2013, Volume 150, Issue 4, pp 678-703.
19-Critical Gaussian multiplicative chaos: Convergence of the derivative martingale , with B.Duplantier, S.Sheffield and V.Vargas, Annals of Probability, Volume 42, Number 5 (2014), 1769-1808.
18-Limiting laws of supercritical branching random walks , with J.Barral and V.Vargas, Comptes rendus - Mathematique 350 (2012) pp. 535-538.
17-Gaussian multiplicative chaos and KPZ duality , with J.Barral, X. Jin, and V.Vargas, Comm. in Math. Physics, October 2013, Volume 323, Issue 2, pp 451-485.
16-Levy multiplicative chaos and star scale invariant random measures, with J.Sohier and V.Vargas, Annals of Probability, Volume 42, Number 2 (2014), 689-724.
15-Marchenko Pastur type theorem for independent MRW processes: convergence of the empirical spectral measure, with R.Allez and V.Vargas, to appear in ESAIM PS.
14-Lognormal scale invariant random measures, with R.Allez and V.Vargas, Probability Theory and Related Fields, April 2013, Volume 155, Issue 3-4, pp 751-788.
13-Optimal transportation for multifractal random measures, applications, with V.Vargas, Annales de l'Institut Henri Poincaré PS, Volume 49, Number 1 (2013), 119-137.
12-Forecasting volatility in the presence of leverage effect, with J.C. Domenge and V.Vargas.
11-Critical homogenization of Itô-Levy process driven SDEs in random medium, with B. Sow, Stochastic Analysis and Applications, Volume 29, Issue 5, 2011.
10-Multidimensional Multifractal Random Measures, with V.Vargas, Electronic Journal of Probability, 2010, Vol 15, 241-258.
9-Scaling limits for symmetric Itô-Lévy processes in random medium, with V.Vargas, Stochastic Processes and their Applications, volume 119, no 12, 2009.
8-KPZ formula for log-infinitely divisible multifractal random measures, with V. Vargas, ESAIM PS, 2011, Vol 15, 358-371.
7-Stochastic Homogenization of Reflected Diffusion ProcessesElectronic Journal of Probability, 2010, vol 15, 989-1023.
6-
Homogenization of periodic semilinear parabolic degenerate PDEs, with E. Pardoux and B. Sow, Annales de l'Institut Henri Poincaré ANL, Vol 26, Issue 3, May-June 2009, 978-998.
5-
Stochastic Homogenization of Quasilinear PDEs with a spatial degeneracy,  with F. Delarue, Asymptotic Analysis, 2009, 61, 61-90.
4-
Homogenization of locally ergodic diffusions with possibly degenerate diffusion matrixAnnales de l'Insitut Henri Poincaré PS, Volume 45, Number 4 (2009), 981-1001.
3-
Diffusion in a Locally Stationary Random Environment,  Probability Theory and Related Fields, Vol 143, No 3-4, 2009, p. 545-568.
2-
Homogenization of space-time dependent and degenerate random flows IIAnnales de l'Institut Henri Poincaré (PS) 2008, vol. 44, n.4, p. 673-692.
1-Homogenization of space-time dependent and degenerate random flows, Stochastic Processes and their Applications, 117 (2007), pages 1561-1585.