The main work of our group is in probability theory, in the domain of random planar geometry. We study random curves, surfaces and other random geometric structures, that help to geometrically encode and describe the large-scale behaviour of complex systems like, for example, 2D statistical physics models.
In particular, we are interested in objects like the Gaussian free field, Schramm-Loewner Evolution, Gaussian multiplicative chaos, Nodal lines of random functions, O(n) spin models, Yang-Mills measures…but this list is not exhaustive and is growing!
We also take interest in other domains of pure mathematics, and are happy if we manage to contribute to research in applied domains like computer science or neurosciences.
Publications in mathematics
Preprints
- J. Aru, N. Holden, E. Powell and X. Sun, Mating of trees for critical Liouville quantum gravity
- M. Ingremeau, A. Rivera, How Lagrangian states evolve into random waves
- S. Muirhead, A. Rivera, H. Vanneuville and L. Köhler-Schindler, The phase transition for planar Gaussian percolation models without FKG
- J. Junnila, E. Saksman and L. Viitasaari, On the regularity of complex multiplicative chaos
Publications
- J. Aru and E. Powell, A characterisation of the continuum Gaussian free field in d≥2 J. Ecol. Polytech, 2022
- J. Aru, A. Jego and J. Junnila, Density of imaginary chaos via Malliavin calculus Probab. Theory Related Fields, 2022
- J. Aru, T. Lupu and A. Sepúlveda, Extremal distance of a CLE_4 loop Ann. of Prob., 2022
- J. Aru and J. Junnila, Reconstructing the base field from imaginary multiplicative chaos Bull. London Math. Soc., 2021
- J. Aru, T. Lupu and A. Sepúlveda, First passage sets of the 2D continuum Gaussian free field: convergence and isomorphisms Comm. Math. Phys., 2020
- J. Aru, C. Groenland, T. Johnston, B. Narayanan, A. Roberts, A. Scott, Exceptional graphs for the random walk 2019, Ann. I. H. Poincare. Pr., 2020
- J. Aru, E. Powell and A. Sepúlveda, Liouville measure as a multiplicative cascade via level sets of the Gaussian free field Ann. Inst. Fourier., 2020
- J. Aru, Gaussian multiplicative chaos through the lens of the 2D Gaussian free field IRS 2017 special issue in Markov. Process Relat., 2020
- J. Aru, T. Lupu and A. Sepúlveda, First passage sets of the 2D continuum Gaussian free field Probab. Theory Related Fields, 2019
- J. Aru, E. Powell and A. Sepúlveda, Critical Liouville measure as a limit of subcritical measures Electron. Commun. Probab., 2019
- J. Aru and A. Sepúlveda, Two-valued local sets of the 2D continuum Gaussian free field: connectivity, labels and induced metrics Electron. J. Probab., 2018
- J. Aru, B. Narayanan, A. Scott and R. Venkatesan, Balancing sums of random vectors Discrete Analysis, 2018.
- J. Aru, Y. Huang and X. Sun, Two perspectives of the 2D unit area quantum sphere and their equivalence Comm. Math. Phys. 356, 261-283, 2017.
- J. Aru, A. Sepúlveda and W. Werner, On bounded-type thin local sets of the two-dimensional Gaussian free field J. Inst. Math. Jussieu, 2017.
- J. Aru, KPZ relation does not hold for the level lines and SLE_\kappa flow lines of the Gaussian free field Probab. Theory Related Fields 163(3-4), 465-526, 2015.
Publications in applied domains
Publications
- A. Tampuu, T. Matiisen, D. Kodelja, I. Kuzovkin, K. Korjus, J. Aru, R. Vicente, Multiagent cooperation and competition with deep reinforcement learning PLOS One 12(4), 2017.
- J. Aru, J. Aru, V. Priesemann, M. Wibral, L. Lana, G. Pipa, W. Singer, R. Vicente, Untangling cross-frequency coupling in neuroscience. Curr. Opin. Neurobiol 31, 2015.
- L. Perie, J. Aru, JJ. Slotine, P. Kourilsky, Does a quorum sensing mechanism direct the behaviour of immune cells C. R. Biol. 336(1), 2013.
- K. Laane, J. Aru, A. Dickinson, Non-competitive liking for brands. No blocking in evaluative conditioning. Appetite 54(1), 2010.