Titus Lupu

Contact

CNRS researcher
Working at LPSM (Laboratoire de Probabilités, Statistique et Modélisation), UMR 8001, at Sorbonne Université (Jussieu)
Member of the 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 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. arXiv:2403.03040.
Conformally invariant fields out of Brownian loop soups. A. Jégo, T. Lupu and W. Qian, 2023. arXiv:2307.10740.
Excursion decomposition of the 2D continuum GFF. J. Aru, T. Lupu and A. Sepúlveda, 2023. arXiv:2304.03150.
Crossing exponent in the Brownian loop soup. A. Jégo, T. Lupu and W. Qian, 2023. arXiv:2303.03782.
An equivalence between gauge-twisted and topologically conditioned scalar Gaussian free fields. T. Lupu, 2022. arXiv:2209.07901.

Publications

A level line of the Gaussian free field with measure-valued boundary conditions. T. Lupu et H. Wu. Science China Mathematics 67, pp. 367–404, 2024. arXiv:2106.15169.
Multiplicative chaos of the Brownian loop soup. E. Aïdékon, N. Berestycki, A. Jégo and T. Lupu. Proceedings of the London Mathematical Society 126 (4), pp. 1254-1393, 2023. arXiv:2107.13340.
Extremal distance and conformal radius of a CLE_4 loop. J. Aru, T. Lupu and A. Sepúlveda. The Annals of Probability 50 (2), pp. 509-558, 2022. arXiv:2004.13570.
Isomorphisms of β-Dyson's Brownian motion with Brownian local time. T. Lupu. Electronic Journal of Probability 26, pp. 1-31, 2021. arXiv:2009.03026.
Topological expansion in isomorphism theorems between matrix-valued fields and random walks. T. Lupu. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 58(2), pp. 695-721, 2022. arXiv:1908.06732.
Inverting the Ray-Knight identity on the line. T. Lupu, C. Sabot and P. Tarrès. Electronic Journal of Probability 26, pp. 1-25, 2021. arXiv:1910.06836.
Fine mesh limit of the VRJP in dimension one and Bass-Burdzy flow. T. Lupu, C. Sabot and P. Tarrès. Probability Theory and Related Fields 177, pp. 55-90, 2020. arXiv:1803.10626.
The first passage sets of the 2D Gaussian free field: convergence and isomorphisms. J. Aru, T. Lupu and A. Sepúlveda. Communications in Mathematical Physics 375, pp. 1885-1929, 2020. arXiv:1805.09204.
First passage sets of the 2D continuum Gaussian free field. J. Aru, T. Lupu and A. Sepúlveda. Probability Theory and Related Fields 176, pp. 1303-1355, 2020. arXiv:1706.07737.
Inverting the coupling of the signed Gausssian free field with a loop soup. T. Lupu, C. Sabot and P. Tarrès. Electronic Journal of Probability 24 (70), pp. 1-28, 2019. 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. Probability Theory and Related Fields 171, pp. 775-818, 2018. arXiv:1607.06424.
A note on Ising random currents, Ising-FK, loop-soups and the Gaussian free field. T. Lupu and W. Werner. Electronic Communications in Probability 21 (13), pp. 1-7, 2016. arXiv:1511.05524.
Convergence of the two-dimensional random walk loop soup clusters to CLE. T. Lupu. Journal of European Mathematical Society 21 (4), pp. 1201-1227, 2019. arXiv:1502.06827.
Loop percolation on discrete half-plane. T. Lupu. Electrononic Communications in Probability 21 (30), pp. 1-9, 2016. arXiv:1408.1045.
From loop clusters and random interlacement to the free field. T. Lupu. The Annals of Probability 44 (3), pp. 2117-2146, 2016. arXiv:1402.0298.
Poisson ensembles of loops of one-dimensional diffusions. T. Lupu. Mémoires de la Société Mathématique de France 158, pp. 1-158, 2018. arXiv:1302.3773.
The Vervaat transform of Brownian bridges and Brownian motion. T. Lupu, J. Pitman and W. Tang. Electronic Journal of Probability 20 (51), pp. 1-31, 2015. arXiv:1310.3889.

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