|[[en|This page in English]] | ====== Titus Lupu ====== {{:users:tlupu:photo_titus.jpg?150|}} ==== Contact ==== Chargé de recherche [[https://www.insmi.cnrs.fr/fr|CNRS]]\\ En poste au [[https://www.lpsm.paris/|LPSM]] (Laboratoire de Probabilités, Statistique et Modélisation), UMR 8001, à [[https://www.sorbonne-universite.fr/|Sorbonne Université]]\\ Membre de l'équipe [[https://www.lpsm.paris/equipes/as/index|Analyse Stochastique]]\\ Courriel : titus dot lupu at sorbonne-universite dot fr\\ Adresse postale : Sorbonne Université, LPSM – 4, place Jussieu – 75005 Paris\\ Bureau : 16-26 210 ==== Enseignement ==== M2: Mécanique statistique critique en dimension 2 et invariance conforme. Cours assuré avec [[https://perso.lpsm.paris/~boutillier/|Cédric Boutillier]]. ==== Recherche ==== === Thèmes de recherche === Je m'intéresse aux structures géométriques intrinséques derrières les champs aléatoires issus de la physique statistique, en particulier en dimension 2 en lien avec l'invariance conforme. Mes recherches touchent au champ libre gaussien et ses représentations par marches aléatoires et mouvement brownien, soupes de boucles browniennes, percolations longue portée, champs permanentaux, champs log-corrélés, chaos multiplicatif gaussien, renormalisation de Wick, processus SLE, marches aléatoires en auto-intéraction, processus stochastiques déterminantaux. === Prépublications === * **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 et W. Qian, 2023. [[https://arxiv.org/abs/2307.10740|arXiv:2307.10740.]] * **Excursion decomposition of the 2D continuum GFF.** J. Aru, T. Lupu et A. Sepúlveda, 2023. [[https://arxiv.org/abs/2304.03150|arXiv:2304.03150.]] * **Crossing exponent in the Brownian loop soup.** A. Jégo, T. Lupu et 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 et 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 et 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 et 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 et 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 et 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 et 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 et 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 et 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 et 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 et 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.]] === Coauteurs === * [[https://www.iufrance.fr/les-membres-de-liuf/membre/1845-elie-aidekon.html|Elie Aïdekon]] * [[https://people.epfl.ch/juhan.aru|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]]