|[[index|Cette page en français]] | ====== Titus Lupu ====== {{:users:tlupu:photo_titus.jpg?150|}} ==== Contact ==== [[https://www.insmi.cnrs.fr/en|CNRS]] researcher\\ Working at [[https://www.lpsm.paris/en/index|LPSM]] (Laboratoire de Probabilités, Statistique et Modélisation), UMR 8001, at [[https://www.sorbonne-universite.fr/en|Sorbonne Université]] (Jussieu)\\ Member of the [[https://www.lpsm.paris/en/equipes/as/index|Stochastic Analysis]] team\\ E-mail : titus dot lupu at sorbonne-universite dot fr\\ Postal address : Sorbonne Université, LPSM – 4, place Jussieu – 75005 Paris\\ Office : 16-26 210 ==== Teaching ==== M2: Mécanique statistique critique en dimension 2 et invariance conforme (Critical statistical mechanics in dimension 2 and conformal invariance). With [[https://perso.lpsm.paris/~boutillier/|Cédric Boutillier]]. ==== Research ==== === Research topics === I am interested in intrinsical geometrical structures behind the random fields originating from statistical physics, in particular in dimension 2 in relation to the conformal invariance. My research involves the Gaussian free field and its random walk and Brownian motion representations, Brownian loop soups, long range percolations, permanental fields, log-correlated fields, Gaussian multiplicative chaos, Wick renormalization, SLE processes, self-interacting random walks, determinantal stochastic processes. === Preprints === * **The height gap of planar Brownian motion is 5/π.** A. Jégo, T. Lupu et W. Qian, 2024. [[https://arxiv.org/abs/2403.03040|arXiv:2403.03040.]] * **Conformally invariant fields out of Brownian loop soups.** A. Jégo, T. Lupu and W. Qian, 2023. [[https://arxiv.org/abs/2307.10740|arXiv:2307.10740.]] * **Excursion decomposition of the 2D continuum GFF.** J. Aru, T. Lupu and A. Sepúlveda, 2023. [[https://arxiv.org/abs/2304.03150|arXiv:2304.03150.]] * **Crossing exponent in the Brownian loop soup.** A. Jégo, T. Lupu and W. Qian, 2023. [[https://arxiv.org/abs/2303.03782|arXiv:2303.03782.]] * **An equivalence between gauge-twisted and topologically conditioned scalar Gaussian free fields.** T. Lupu, 2022. [[https://arxiv.org/abs/2209.07901|arXiv:2209.07901.]] === Publications === * **A level line of the Gaussian free field with measure-valued boundary conditions.** T. Lupu et H. Wu. //[[https://link.springer.com/article/10.1007/s11425-021-2081-8|Science China Mathematics]]// 67, pp. 367–404, 2024. [[https://arxiv.org/abs/2106.15169|arXiv:2106.15169.]] * **Multiplicative chaos of the Brownian loop soup.** E. Aïdékon, N. Berestycki, A. Jégo and T. Lupu. //[[https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12511|Proceedings of the London Mathematical Society]]// 126 (4), pp. 1254-1393, 2023. [[https://arxiv.org/abs/2107.13340|arXiv:2107.13340.]] * **Extremal distance and conformal radius of a CLE_4 loop.** J. Aru, T. Lupu and A. Sepúlveda. //[[https://projecteuclid.org/journals/annals-of-probability/volume-50/issue-2/Extremal-distance-and-conformal-radius-of-a-CLE4-loop/10.1214/21-AOP1538.short|The Annals of Probability]]// 50 (2), pp. 509-558, 2022. [[https://arxiv.org/abs/2004.13570|arXiv:2004.13570.]] * **Isomorphisms of β-Dyson's Brownian motion with Brownian local time.** T. Lupu. //[[https://projecteuclid.org/journals/electronic-journal-of-probability/volume-26/issue-none/Isomorphisms-of-%ce%b2-Dysons-Brownian-motion-with-Brownian-local-time/10.1214/21-EJP697.full|Electronic Journal of Probability]]// 26, pp. 1-31, 2021. [[https://arxiv.org/abs/2009.03026|arXiv:2009.03026.]] * **Topological expansion in isomorphism theorems between matrix-valued fields and random walks.** T. Lupu. //[[https://projecteuclid.org/journals/annales-de-linstitut-henri-poincare-probabilites-et-statistiques/volume-58/issue-2/Topological-expansion-in-isomorphism-theorems-between-matrix-valued-fields-and/10.1214/21-AIHP1198.short|Annales de l'Institut Henri Poincaré, Probabilités et Statistiques]]// 58(2), pp. 695-721, 2022. [[https://arxiv.org/abs/1908.06732|arXiv:1908.06732.]] * **Inverting the Ray-Knight identity on the line.** T. Lupu, C. Sabot and P. Tarrès. //[[https://projecteuclid.org/journals/electronic-journal-of-probability/volume-24/issue-none/Inverting-the-coupling-of-the-signed-Gaussian-free-field-with/10.1214/19-EJP326.full|Electronic Journal of Probability]]// 26, pp. 1-25, 2021. [[https://arxiv.org/abs/1910.06836|arXiv:1910.06836.]] * **Fine mesh limit of the VRJP in dimension one and Bass-Burdzy flow.** T. Lupu, C. Sabot and P. Tarrès. //[[https://link.springer.com/article/10.1007/s00440-019-00944-y|Probability Theory and Related Fields]]// 177, pp. 55-90, 2020. [[https://arxiv.org/abs/1803.10626|arXiv:1803.10626.]] * **The first passage sets of the 2D Gaussian free field: convergence and isomorphisms.** J. Aru, T. Lupu and A. Sepúlveda. //[[https://link.springer.com/article/10.1007/s00220-020-03718-z|Communications in Mathematical Physics]]// 375, pp. 1885-1929, 2020. [[https://arxiv.org/abs/1805.09204|arXiv:1805.09204.]] * **First passage sets of the 2D continuum Gaussian free field.** J. Aru, T. Lupu and A. Sepúlveda. //[[https://link.springer.com/article/10.1007/s00440-019-00941-1|Probability Theory and Related Fields]]// 176, pp. 1303-1355, 2020. [[https://arxiv.org/abs/1706.07737|arXiv:1706.07737.]] * **Inverting the coupling of the signed Gausssian free field with a loop soup.** T. Lupu, C. Sabot and P. Tarrès. //[[https://projecteuclid.org/journals/electronic-journal-of-probability/volume-24/issue-none/Inverting-the-coupling-of-the-signed-Gaussian-free-field-with/10.1214/19-EJP326.full|Electronic Journal of Probability]]// 24 (70), pp. 1-28, 2019. [[https://arxiv.org/abs/1701.01092|arXiv:1701.01092.]] * **The random pseudo-metric on a graph defined via the zero-set of the Gaussian free field on its metric graph.** T. Lupu and W. Werner. //[[https://link.springer.com/article/10.1007/s00440-017-0792-y|Probability Theory and Related Fields]]// 171, pp. 775-818, 2018. [[https://arxiv.org/abs/1607.06424|arXiv:1607.06424.]] * **A note on Ising random currents, Ising-FK, loop-soups and the Gaussian free field.** T. Lupu and W. Werner. //[[https://projecteuclid.org/journals/electronic-communications-in-probability/volume-21/issue-none/A-note-on-Ising-random-currents-Ising-FK-loop-soups/10.1214/16-ECP4733.full|Electronic Communications in Probability]]// 21 (13), pp. 1-7, 2016. [[https://arxiv.org/abs/1511.05524|arXiv:1511.05524.]] * **Convergence of the two-dimensional random walk loop soup clusters to CLE.** T. Lupu. //[[https://ems.press/journals/jems/articles/15964|Journal of European Mathematical Society]]// 21 (4), pp. 1201-1227, 2019. [[https://arxiv.org/abs/1502.06827|arXiv:1502.06827.]] * **Loop percolation on discrete half-plane.** T. Lupu. //[[https://projecteuclid.org/journals/electronic-communications-in-probability/volume-21/issue-none/Loop-percolation-on-discrete-half-plane/10.1214/16-ECP4571.full|Electrononic Communications in Probability]]// 21 (30), pp. 1-9, 2016. [[https://arxiv.org/abs/1408.1045|arXiv:1408.1045.]] * **From loop clusters and random interlacement to the free field.** T. Lupu. //[[https://projecteuclid.org/journals/annals-of-probability/volume-44/issue-3/From-loop-clusters-and-random-interlacements-to-the-free-field/10.1214/15-AOP1019.full|The Annals of Probability]]// 44 (3), pp. 2117-2146, 2016. [[https://arxiv.org/abs/1402.0298|arXiv:1402.0298.]] * **Poisson ensembles of loops of one-dimensional diffusions.** T. Lupu. //[[https://smf.emath.fr/publications/ensembles-poissoniens-de-boucles-des-diffusions-unidimensionnelles|Mémoires de la Société Mathématique de France]]// 158, pp. 1-158, 2018. [[https://arxiv.org/abs/1302.3773|arXiv:1302.3773.]] * **The Vervaat transform of Brownian bridges and Brownian motion.** T. Lupu, J. Pitman and W. Tang. //[[https://projecteuclid.org/journals/electronic-journal-of-probability/volume-20/issue-none/The-Vervaat-transform-of-Brownian-bridges-and-Brownian-motion/10.1214/EJP.v20-3744.full|Electronic Journal of Probability]]// 20 (51), pp. 1-31, 2015. [[https://arxiv.org/abs/1310.3889|arXiv:1310.3889.]] === Coauthors === * [[https://www.iufrance.fr/les-membres-de-liuf/membre/1845-elie-aidekon.html|Elie Aïdekon]] * [[https://people.epfl.ch/juhan.aru/?lang=en|Juhan Aru]] * [[https://homepage.univie.ac.at/nathanael.berestycki/|Nathanaël Berestycki]] * [[http://www.normalesup.org/~ajego/|Antoine Jégo]] * [[https://www.stat.berkeley.edu/~pitman/|Jim Pitman]] * [[https://qian.perso.math.cnrs.fr/|Wei Qian]] * [[http://math.univ-lyon1.fr/homes-www/sabot/|Christophe Sabot]] * [[http://www.dim.uchile.cl/~lsepulveda/|Avelio Sepúlveda]] * [[http://www.columbia.edu/~wt2319/|Wenpin Tang]] * [[https://www.ceremade.dauphine.fr/~tarres/|Pierre Tarrès]] * [[https://www.dpmms.cam.ac.uk/~ww295/|Wendelin Werner]] * [[https://qzc.tsinghua.edu.cn/en/info/1169/1898.htm|Hao Wu]]