References

• Barral, Julien; Jin, Xiong; Rhodes, Rémi; Vargas, Vincent. Gaussian multiplicative chaos and KPZ duality. Comm. Math. Phys. 323 (2013), no. 2, 451--485. MR3096527
• Barral, Julien; Mandelbrot, Benoît B. Introduction to infinite products of independent random functions (Random multiplicative multifractal measures. I). Fractal geometry and applications: a jubilee of Benoît Mandelbrot, Part 2, 3--16, Proc. Sympos. Pure Math., 72, Part 2, Amer. Math. Soc., Providence, RI, 2004. MR2112119
• Benjamini, Itai; Schramm, Oded. KPZ in one dimensional random geometry of multiplicative cascades. Comm. Math. Phys. 289 (2009), no. 2, 653--662. MR2506765
• Berestycki N.: Diffusion in planar Liouville quantum gravity, arXiv:1301.3356.
• Biroli, Marco; Mosco, Umberto. Formes de Dirichlet et estimations structurelles dans les milieux discontinus. (French) [Dirichlet forms and structural estimates in discontinuous media] C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 9, 593--598. MR1133491
• Biroli, M.; Mosco, U. A Saint-Venant type principle for Dirichlet forms on discontinuous media. Ann. Mat. Pura Appl. (4) 169 (1995), 125--181. MR1378473
• David, F. Conformal field theories coupled to $2$-D gravity in the conformal gauge. Modern Phys. Lett. A 3 (1988), no. 17, 1651--1656. MR0981529
• Davies, E. B. Heat kernels and spectral theory. Cambridge Tracts in Mathematics, 92. Cambridge University Press, Cambridge, 1989. x+197 pp. ISBN: 0-521-36136-2 MR0990239
• Di Francesco, P.; Ginsparg, P.; Zinn-Justin, J. $2$D gravity and random matrices. Phys. Rep. 254 (1995), no. 1-2, 133 pp. MR1320471
• Distler, Jacques; Kawai, Hikaru. Conformal field theory and $2$D quantum gravity. Nuclear Phys. B 321 (1989), no. 2, 509--527. MR1005268
• Duplantier, Bertrand; Sheffield, Scott. Liouville quantum gravity and KPZ. Invent. Math. 185 (2011), no. 2, 333--393. MR2819163
• Duplantier B., Rhodes R., Sheffield S., Vargas V.: Critical Gaussian multiplicative chaos: convergence of the derivative martingale, to appear in phAnnals of Probability, arXiv:1206.1671.
• Duplantier B., Rhodes R., Sheffield S., Vargas V.: Renormalization of Critical Gaussian Multiplicative Chaos and KPZ formula, to appear in phCommunications in Mathematical Physics, arXiv:1212.0529.
• Fukushima, Masatoshi; Ōshima, Yōichi; Takeda, Masayoshi. Dirichlet forms and symmetric Markov processes. de Gruyter Studies in Mathematics, 19. Walter de Gruyter & Co., Berlin, 1994. x+392 pp. ISBN: 3-11-011626-X MR1303354
• Garban C, Rhodes R., Vargas V.: Liouville Brownian motion, arXiv:1301.2876v2.
• Ginsparg P. and Moore G.: Lectures on 2D gravity and 2D string theory, in textitRecent direction in particle theory, Proceedings of the 1992 TASI, edited by J. Harvey and J. Polchinski (World Scientific, Singapore, 1993).
• Hino, Masanori. Measurable Riemannian structures associated with strong local Dirichlet forms. Math. Nachr. 286 (2013), no. 14-15, 1466--1478. MR3119694
• Hu, Xiaoyu; Miller, Jason; Peres, Yuval. Thick points of the Gaussian free field. Ann. Probab. 38 (2010), no. 2, 896--926. MR2642894
• Kahane, Jean-Pierre. Sur le chaos multiplicatif. (French) [Multiplicative chaos] Ann. Sci. Math. Québec 9 (1985), no. 2, 105--150. MR0829798
• Kakutani, Shizuo. Two-dimensional Brownian motion and harmonic functions. Proc. Imp. Acad. Tokyo 20, (1944). 706--714. MR0014647
• Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1988. xxiv+470 pp. ISBN: 0-387-96535-1 MR0917065
• Kim, Panki; Song, Renming; Vondraček, Zoran. On harmonic functions for trace processes. Math. Nachr. 284 (2011), no. 14-15, 1889--1902. MR2838289
• Knizhnik, V. G.; Polyakov, A. M.; Zamolodchikov, A. B. Fractal structure of $2$D-quantum gravity. Modern Phys. Lett. A 3 (1988), no. 8, 819--826. MR0947880
• Nakayama, Yu. Liouville field theory: a decade after the revolution. Internat. J. Modern Phys. A 19 (2004), no. 17-18, 2771--2930. MR2073993
• Revuz D.: Remarque sur les potentiels de mesures, phSéminaire de probabilités (Strasbourg) 5, 275-277 (1971).
• Rhodes, Rémi; Vargas, Vincent. KPZ formula for log-infinitely divisible multifractal random measures. ESAIM Probab. Stat. 15 (2011), 358--371. MR2870520
• Rhodes R., Vargas, V.: Gaussian multiplicative chaos and applications: a review, arXiv:1305.6221.
• Robert, Raoul; Vargas, Vincent. Hydrodynamic turbulence and intermittent random fields. Comm. Math. Phys. 284 (2008), no. 3, 649--673. MR2452591
• Robert, Raoul; Vargas, Vincent. Gaussian multiplicative chaos revisited. Ann. Probab. 38 (2010), no. 2, 605--631. MR2642887
• Stollmann, Peter. A dual characterization of length spaces with application to Dirichlet metric spaces. Studia Math. 198 (2010), no. 3, 221--233. MR2650987
• Sturm, Karl-Theodor. Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and $L^ p$-Liouville properties. J. Reine Angew. Math. 456 (1994), 173--196. MR1301456
• Sturm, Karl-Theodor. The geometric aspect of Dirichlet forms. New directions in Dirichlet forms, 233--277, AMS/IP Stud. Adv. Math., 8, Amer. Math. Soc., Providence, RI, 1998. MR1652282
• Varopoulos, N. Th.; Saloff-Coste, L.; Coulhon, T. Analysis and geometry on groups. Cambridge Tracts in Mathematics, 100. Cambridge University Press, Cambridge, 1992. xii+156 pp. ISBN: 0-521-35382-3 MR1218884
• Yan, Jia An. A formula for densities of transition functions. Séminaire de Probabilités, XXII, 92--100, Lecture Notes in Math., 1321, Springer, Berlin, 1988. MR0960514