Dominique Malicet
Associate professor (Maître de conférences) of Mathematics
Université Gustave Eiffel, LAMA
email: dominique.malicet[at]univ-eiffel.fr

Topics of research

-Dynamical systems and ergodic theory:
I am interested in the study of group actions and random dynamical sysytems on manifolds of small dimension. I am trying to exhibit hyperbolicity phenomena (e.g. study of the Lyapunov exponents), conditions of reduction (e.g. KAM reduction, invariance principles) and structure of group actions (e.g. Markov partitions, Ping-pong structures).

-Functional analysis in probability:
I am working in the study of non linear functionals of random variables by the mean of functional calculus technics (e.g. Dirichlet and Malliavin's calculus, Wiener's chaos decompositions), in particular to establish properties of the distribution measures, concentration and anticoncentration phenomena, central limit theorems.

ANR project

I participate the ANR project Gromeov, on the study of group actions on manifolds of small dimensions, supervised by Michele Triestino and Victor Kleptsyn.

Responsabilities

I organize the analysis seminar of the LAMA with Colin Petitjean [page]

Publications

1-"Properties of convergence in Dirichlet structures", Journal of Functional Analysis, 2013, vol. 264, no 9, p. 2077-2096 (with G. Poly)
[Journal]
2-"Generalization of the Nualart–Peccati criterion", The Annals of Probability, 2016, vol. 44, no 2, p. 924-954 (with E.Azmoodeh, G.Mijoule and G.Poly)
[Journal] [arxiv]
3-"Squared chaotic random variables: new moment inequalities with applications", Journal of Functional Analysis, 2016, vol. 270, no 2, p. 649-670 (with I.Nourdin, G.Peccati and G.Poly)
[Journal] [arxiv]
4-"Random walks on Homeo(S1)", Communications in Mathematical Physics, 2017, vol. 356, p. 1083-1116
[Journal] [arxiv]
5-"Expanding actions: minimality and ergodicity", Stochastics and Dynamics, 2017, vol. 17, no 04 (with P.G.Barrientos, A.Fakhari and A.Sarizadeh)
[Journal] [arxiv]
6-"On the chaos game of iterated function systems", Topological Methods in Nonlinear Analysis, 2017, vol. 49, no 1, p.105-132 (with P.G.Barrientos, F.H.Ghane, A.Sarizadeh)
[Journal] [arxiv]
7-"Groups with infinitely many ends acting analytically on the circle", Journal of topology, 2019, vol. 12, no 4, p. 1315-1367 (with S.Alvarez, D.Filimonov, V.Kleptsyn, D.Malicet, C.Meniño, A.Navas and M.Triestino)
[Journal] [arxiv]
8-"Ping-pong configurations and circular orders on free groups", Groups, Geometry, and Dynamics, 2019, vol. 13, no 4, p. 1195-1218 (with K Mann, C Rivas, M Triestino)
[Journal] [arxiv]
9-"Extremal exponents of random products of conservative diffeomorphisms", Mathematische Zeitschrift, 2020, vol. 296, no 3-4, p. 1185-1207 (with Pablo Barrientos)
[Journal] [arxiv]
10-"Lyapunov exponent of random dynamical systems on the circle", Ergodic Theory and Dynamical Systems, 2022, vol. 42, no 6, p. 2080-2107
[Journal] [arxiv]

Preprints

1-"Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction", 2019 (with J.Alonso,S.Alvarez,C.Meniño and M.Triestino)
[arxiv]
2-"Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, II: Applications", 2021 (with S.Alvarez, P.G.Barrientos, D.Filimonov, V.Kleptsyn, C.Meniño and M.Triestino)
[arxiv]
3-"A short proof of the strong three dimensional Gaussian product inequality", 2022, accepted in Proc. of AMS (with R.Herry and G.Poly)
[arxiv]
4-"Groups of smooth diffeomorphisms of Cantor sets embedded in a line", 2023 (with E. Militon)
[arxiv]
5-"Almost sure behavior of the critical points of random polynomials", 2023 (with J.Angst and G.Poly)
[arxiv]
6-"Regularity of laws via Dirichlet forms--Application to quadratic forms in independent and identically distributed random variables", 2023 (with R.Herry and G.Poly)
[arxiv]
7-"Central convergence on Wiener chaoses always implies asymptotic smoothness and C^infinity convergence of densities", 2023 (with R.Herry and G.Poly)
[arxiv]

PhD thesis

Title: Exposants de Lyapunov de systemes dynamiques aleatoires sur le tore
Advisor: Raphaël Krikorian
Place: Sorbonne Université
Year of defense: 2012
Reviewers: Konstantin Khanin and Jean-Cristophe Yoccoz
Jury: Artur Ávila, Sylvain Crovisier, Dmitry Dolgopyat, Bassam Fayad, Yves Le Jan and Jean-Paul Thouvenot
PDF: [here]

Miscellaneous notes :

-"The 2x-3x theorem of Furstenberg", appendix chapter for the text "Entropy, Lyapunov exponents, and rigidity of group actions" of A.Brown, in Ensaios Matemáticos, 2019, vol. 33
[here], [integral text]
-"Série de Riemann à exposant oscillant", analysis topic for "Concours SMF junior" 2022 (french)
[questions], [solution]