L. F. Alday, D. Gaiotto, and Y. Tachikawa, Liouville Correlation Functions from Four-Dimensional Gauge Theories, Letters in Mathematical Physics, vol.10, issue.2, pp.167-197, 2010.
DOI : 10.1007/978-1-4612-2256-9

URL : http://arxiv.org/abs/0906.3219

J. Aru, Y. Huang, and X. Sun, Two Perspectives of the 2D Unit Area Quantum Sphere and Their Equivalence, Communications in Mathematical Physics, vol.44, issue.5
DOI : 10.1214/15-AOP1055

A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nuclear Physics B, vol.241, issue.2, pp.333-380, 1984.
DOI : 10.1016/0550-3213(84)90052-X

N. Berestycki, An elementary approach to Gaussian multiplicative chaos, Electronic Communications in Probability, vol.22, issue.0, pp.1-12, 2017.
DOI : 10.1214/17-ECP58

URL : http://doi.org/10.1214/17-ecp58

A. Borodin and P. Salminen, Handbook of Brownian motion-Facts and Formulae, Probability and Its Applications, 1996.

C. Boutillier and B. Detilì-ere, The critical Z-invariant Ising model via dimers: the periodic case, Probability Theory and related fields 147, pp.379-413, 2010.

C. Boutillier and B. Detilì-ere, The Critical Z-Invariant Ising Model via Dimers: Locality Property, Communications in Mathematical Physics, vol.65, issue.3-4, pp.473-516, 2011.
DOI : 10.4159/harvard.9780674180758

URL : https://hal.archives-ouvertes.fr/hal-00361365

D. Chelkak, A. Glazman, and S. Smirnov, Discrete stress-energy tensor in the loop O(n) model

D. Chelkak and S. Smirnov, Universality in the 2D Ising model and conformal invariance of fermionic observables, Inventiones mathematicae 189, pp.515-580, 2012.

D. Chelkak, C. Hongler, and K. Izyurov, Conformal invariance of spin correlations in~the~planar Ising model, Annals of Mathematics, vol.181, pp.1087-1138, 2015.
DOI : 10.4007/annals.2015.181.3.5

T. Curtright and C. Thorn, Conformally Invariant Quantization of the Liouville Theory, Physical Review Letters, vol.7, issue.19, p.1309, 1982.
DOI : 10.1103/PhysRevD.7.1732

F. David, A. Kupiainen, R. Rhodes, and V. Vargas, Liouville Quantum Gravity on the Riemann Sphere, Liouville Quantum Gravity on the Riemann sphere, pp.869-907, 2016.
DOI : 10.1016/0550-3213(96)00351-3

URL : https://hal.archives-ouvertes.fr/cea-01509870

H. Dorn and H. Otto, Two- and three-point functions in Liouville theory, Nuclear Physics B, vol.429, issue.2, pp.375-388, 1994.
DOI : 10.1016/0550-3213(94)00352-1

URL : http://arxiv.org/abs/hep-th/9403141

J. Dubédat, SLE and the free field: Partition functions and couplings, Journal of the American Mathematical Society, vol.22, issue.4, pp.995-1054, 2009.
DOI : 10.1090/S0894-0347-09-00636-5

J. Dubédat, Exact bosonization of the Ising model

B. Duplantier, J. Miller, and . Sheffield, Liouville quantum gravity as mating of trees
URL : https://hal.archives-ouvertes.fr/cea-01251995

S. El-showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-duffin et al., Solving the 3D Ising model with the conformal bootstrap, Physical Review D, vol.2, issue.2, p.25022, 2012.
DOI : 10.1016/S0550-3213(02)00739-3

URL : https://hal.archives-ouvertes.fr/cea-00825766

S. El-showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-duffin et al., Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents, Journal of Statistical Physics, vol.44, issue.4-5, p.25022, 2012.
DOI : 10.1007/978-1-4757-2868-2_7

S. Ferrara, A. F. Grillo, and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion, Annals Phys, pp.76-161188, 1973.

P. J. Forrester and S. O. Warnaar, The importance of the Selberg integral, Bulletin of the American Mathematical Society, vol.45, issue.4, pp.489-534, 2008.
DOI : 10.1090/S0273-0979-08-01221-4

Y. Fyodorov and J. Bouchaud, Freezing and extreme-value statistics in a random energy model with logarithmically correlated potential, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.37, p.372001, 2008.
DOI : 10.1088/1751-8113/41/37/372001

Y. Fyodorov, L. Doussal, P. Rosso, and A. , noises generated by Gaussian free fields, Journal of Statistical Mechanics: Theory and Experiment, vol.2009, issue.10, p.10005, 2009.
DOI : 10.1088/1742-5468/2009/10/P10005

URL : https://hal.archives-ouvertes.fr/hal-00423366

K. Gawedzki, Lectures on conformal field theory, Quantum field theory program at IAS

G. R. Grimmett, Percolation, second edition, 1999.

D. Harlow, J. Maltz, and E. Witten, Analytic continuation of Liouville theory, Journal of High Energy Physics, vol.02, issue.12, 2011.
DOI : 10.1007/JHEP02(2010)029

URL : http://arxiv.org/pdf/1108.4417

C. Hongler and S. Smirnov, The energy density in the planar Ising model, Acta Mathematica, vol.211, issue.2, pp.191-225, 2013.
DOI : 10.1007/s11511-013-0102-1

Y. Ikhlef, J. L. Jacobsen, and H. Saleur, Liouville Theory and Conformal Loop Ensembles, Physical Review Letters, vol.116, issue.13, p.130601, 2016.
DOI : 10.1103/PhysRevLett.57.2332

URL : https://hal.archives-ouvertes.fr/cea-01468523

I. Karatzas and S. Shreve, Brownian motion and stochastic calculus

V. G. Knizhnik, A. M. Polyakov, and A. B. Zamolodchikov, Fractal structure of 2D-quantum gravity, Modern Phys, Lett A, vol.3, issue.8, pp.819-826, 1988.

I. K. Kostov and V. B. Petkova, Bulk Correlation Functions in 2d Quantum Gravity, Theoretical and Mathematical Physics, vol.386, issue.1, pp.108-118, 2006.
DOI : 10.1007/s11232-005-0048-3

URL : http://arxiv.org/abs/hep-th/0505078

A. Kupiainen, Constructive Liouville Conformal Field Theory

G. Mack, Duality in quantum field theory, Nuclear Physics B, vol.118, issue.5, p.118, 1977.
DOI : 10.1016/0550-3213(77)90238-3

D. Maulik and A. Okounkov, Quantum Groups and Quantum Cohomology

Y. Nakayama, LIOUVILLE FIELD THEORY: A DECADE AFTER THE REVOLUTION, International Journal of Modern Physics A, vol.29, issue.17n18, pp.2771-2930, 2004.
DOI : 10.1016/S0550-3213(01)00573-9

O. 'raifeartaigh, L. Pawlowski, J. M. Sreedhar, and V. V. , The Two-exponential Li-ouville Theory and the Uniqueness of the Three-point Function, Physics Letters B, vol.481, pp.2-4, 2000.

K. Osterwalder and R. Schrader, Axioms for Euclidean Green's functions, Communications in Mathematical Physics, vol.24, issue.2, pp.83-112, 1973.
DOI : 10.1007/BF01645738

K. Osterwalder and R. Schrader, Axioms for Euclidean Green's functions II, Communications in Mathematical Physics, vol.36, issue.3, pp.281-305, 1975.
DOI : 10.1007/BF01608978

A. M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett, pp.103-207, 1981.

A. M. Polyakov, Nonhamiltonian approach to conformal quantum field theory, Zh. Eksp. Teor. Fiz, vol.66, p.2342, 1974.

G. Rémy, The Fyodorov-Bouchaud formula, work in progress

S. Ribault, Conformal Field theory on the plane
URL : https://hal.archives-ouvertes.fr/cea-01062770

S. Ribault and R. Santachiara, Liouville theory with a central charge less than one, Journal of High Energy Physics, vol.07, issue.8, p.109, 2015.
DOI : 10.1007/JHEP07(2015)054

URL : https://hal.archives-ouvertes.fr/hal-01196718

R. Rhodes and V. Vargas, Gaussian multiplicative chaos and applications: a review, Probability Surveys, pp.315-392, 2014.
DOI : 10.1214/13-ps218

URL : http://arxiv.org/abs/1305.6221

R. Rhodes and V. Vargas, Multidimensional Multifractal Random Measures, Electronic Journal of Probability, vol.15, issue.0, pp.241-258, 2010.
DOI : 10.1214/EJP.v15-746

URL : https://hal.archives-ouvertes.fr/hal-00394758

N. Seiberg, Notes on Quantum Liouville Theory and Quantum Gravity, Progress of Theoretical Physics, 1990.

S. Sheffield, Gaussian free fields for mathematicians, Probab. Th. Rel, pp.521-541, 2007.
DOI : 10.1007/s00440-006-0050-1

URL : http://arxiv.org/abs/math/0312099

S. Smirnov, Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model, Annals of mathematics, vol.172, pp.1435-1467, 2010.

J. Teschner, On the Liouville three-point function, Physics Letters B, vol.363, issue.1-2, pp.65-70, 1995.
DOI : 10.1016/0370-2693(95)01200-A

URL : http://arxiv.org/pdf/hep-th/9507109

J. Teschner, Liouville theory revisited, Classical and Quantum Gravity, vol.18, issue.23, pp.153-222, 2001.
DOI : 10.1088/0264-9381/18/23/201

URL : http://arxiv.org/abs/hep-th/0104158

D. Williams, Path Decomposition and Continuity of Local Time for One-Dimensional Diffusions, I, Proceedings of the London Mathematical Society s3, pp.738-768, 1974.
DOI : 10.1112/plms/s3-28.4.738

A. B. Zamolodchikov, Three-point function in the minimal Liouville gravity, Theoretical and Mathematical Physics, vol.264, issue.2, pp.183-196, 2005.
DOI : 10.1016/0370-2693(91)90351-P

A. B. Zamolodchikov and A. B. Zamolodchikov, Conformal bootstrap in Liouville field theory, Nuclear Physics B, vol.477, issue.2, pp.577-605, 1996.
DOI : 10.1016/0550-3213(96)00351-3