Open Access
Issue
ESAIM: PS
Volume 25, 2021
Page(s) 433 - 459
DOI https://doi.org/10.1051/ps/2021016
Published online 15 November 2021
  1. M. Ang and E. Gwynne, Liouville quantum gravity surfaces with boundary as matings of trees. Ann. Inst. Henri Poincaré Prob. Stat. 57 (2021) 1–53. [Google Scholar]
  2. J. Aru, Y. Huang and X. Sun, Two perspectives of the 2D unit area quantum sphere and their equivalence. Commun. Math. Phys. 356 (2017) 261–283. [Google Scholar]
  3. N. Berestycki, S. Sheffield and X. Sun, Equivalence of Liouville measure and Gaussian free field. Preprint arXiv:1410.5407 (2014). [Google Scholar]
  4. J. Bettinelli and G. Miermont, Compact Brownian surfaces I: Brownian disks. Prob. Theory Related Fields 167 (2017) 555. [Google Scholar]
  5. F. David, A. Kupiainen, R. Rhodes and V. Vargas, Liouville quantum gravity on the Riemann sphere. Commun. Math. Phys. 342 (2016) 869. [Google Scholar]
  6. J. Ding, J. Dubédat, A. Dunlap and H. Falconet, Tightness of Liouville first passage percolation for γ ∈ (0, 2). Publ. Math. l’IHÉS 132 (2020) 353–403. [Google Scholar]
  7. F. David, R. Rhodes and V. Vargas, Liouville quantum gravity on complex tori. J. Math. Phys. 57 (2016) 022302. [Google Scholar]
  8. B. Duplantier and S. Sheffield, Liouville Quantum Gravity and KPZ. Invent. Math. 185 (2011) 333. [Google Scholar]
  9. A. Göing-Jaeschke and M. Yor, A survey and some generalizations of Bessel processes. Bernoulli 9 (2003) 313–349. [Google Scholar]
  10. B. Duplantier, J. Miller and S. Sheffield, Liouville quantum gravity as a mating of trees. Preprint arXiv:1409.7055 (2014). [Google Scholar]
  11. C. Guillarmou, R. Rhodes and V. Vargas, Polyakov’s formulation of 2d bosonic string theory. Publ. Math. l’IHÉS 130 (2016) 111–185. [Google Scholar]
  12. E. Gwynne and J. Miller, Existence and uniqueness of the Liouville quantum gravity metric for γ ∈ (0, 2). Invent. Math. 223 (2021) 213–333. [Google Scholar]
  13. Y. Huang, R. Rhodes and V. Vargas, Liouville quantum gravity on the unit disk. Ann. Inst. Henri Poincaré Probab. Statist. 54 (2018) 1694–1730. [Google Scholar]
  14. S. Janson, Gaussian Hilbert spaces. Cambridge Tracts in Mathematics. Cambridge University Press (1997). [Google Scholar]
  15. J.-P. Kahane, Sur le chaos multiplicatif. Ann. Sci. Math. Québec 9 (1985) 105–150. [Google Scholar]
  16. A. Kupiainen, R. Rhodes and V. Vargas, The DOZZ formula from the path integral. J. High Energy Phys. 94 (2018) 2018. [Google Scholar]
  17. A. Kupiainen, R. Rhodes and V. Vargas, Local conformal structure of liouville quantum gravity. Commun. Math. Phys. 371 (2018) 1005–1069. [Google Scholar]
  18. J.-F. Le Gall Uniqueness and universality of the Brownian map. Ann. Probab. 41 (2013) 2880–2960. [Google Scholar]
  19. G. Miermont, The Brownian map is the scaling limit of uniform random plane quadrangulations. Acta Math. 210 (2013) 319–401. [Google Scholar]
  20. J. Miller and S. Sheffield, Liouville quantum gravity and the Brownian map II: geodesics and continuity of the embedding. Preprint arXiv:1605.03563 (2016). [Google Scholar]
  21. J. Miller and S. Sheffield, Liouville quantum gravity and the Brownian map III: the conformal structure is determined. Preprint arXiv:1608.05391 (2016). [Google Scholar]
  22. J. Miller and S. Sheffield, Imaginary geometry IV: interior rays, whole-plane reversibility, and space-filling trees. Prob. Theory Related Fields 169 (2017) 729. [Google Scholar]
  23. J. Miller and S. Sheffield, Liouville quantum gravity and the Brownian map I: the QLE(8/3, 0) metric. Invent. Math. 219 (2019) 75–152. [Google Scholar]
  24. A. Polyakov, Quantum Geometry of bosonic strings. Phys. Lett. B 103 (1981) 207:210. [Google Scholar]
  25. D. Revuz and M. Yor, Continuous Martingales and Brownian Motion. Springer, Berlin (1991). [Google Scholar]
  26. R. Rhodes and V. Vargas, Gaussian multiplicative chaos and applications: a review. Probab. Surv. 11 (2014) 315–392. [Google Scholar]
  27. R. Rhodes and V. Vargas, Lecture notes on Gaussian multiplicative chaos and Liouville Quantum Gravity. Preprint arXiv:1602.07323 (2016). [Google Scholar]
  28. N. Seiberg, Notes on quantum Liouville theory and quantum gravity. Random Surf. Quant. Grav. 262 (1990) 363. [Google Scholar]
  29. S. Sheffield, Gaussian free field for mathematicians. Prob. Theory Related Fields 139 (2007) 521. [Google Scholar]
  30. S. Sheffield, Conformal weldings of random surfaces: SLE and the quantum gravity zipper. Ann. Probab. 44 (2016) 3474–3545. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.