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Intermediate Chaos

Total Cost €


EC-Contrib. €






 IChaos project word cloud

Explore the words cloud of the IChaos project. It provides you a very rough idea of what is the project "IChaos" about.

math    conjecture    theorems    katok    substitution    central    infinite    translation    last    matrices    2013    preprint    orthogonally    0001    geometric    structures    hamiltonian    exhibit    solution    chaos    geometry    1985    functional    proof    hausdorff    point    borodin    entropy    mix    questions    spectral    decades    ya    dimension    proposer    symbolic    combinatorics    republic    exchange    intermediate    question    02    harmonic    flows    manifold    description    chaotic    idex    2014    annals    2015    genus    2012    360000    government    interval    pi    gafa    quasi    maps    consolidates    intense    mathematical    surfaces    olshanski    asymptotic    crystals    origin    avenir    deterministic    physics    budget    theory    grassmann    arise    french    naturally    dimensional    examples    pfaffian    space    11    decomposition    computation    sinai    posed    determinantal    vershik    arising    limit    investigation    ergodic    anr    theme    investissements    2000    transition    dynamical    invariant    kerov    despite   

Project "IChaos" data sheet

The following table provides information about the project.


Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Project website
 Total cost 1˙696˙936 €
 EC max contribution 1˙696˙936 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-CoG
 Funding Scheme ERC-COG
 Starting year 2016
 Duration (year-month-day) from 2016-01-01   to  2020-12-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

'The transition from order to chaos has been a central theme of investigation in dynamical systems in the last two decades. Structures that exhibit a mix of deterministic and chaotic properties, for example, quasi-crystals, naturally arise in problems of geometry and mathematical physics. Despite intense study, key questions about these structures remain wide open. The proposed research is an investigation of intermediate chaos in ergodic theory of dynamical systems. Specific examples include systems of geometric origin such as interval exchange maps, translation and Hamiltonian flows on surfaces of higher genus, symbolic substitution systems important in the study of quasi-crystals as well as dynamical systems arising in asymptotic combinatorics and mathematical physics such as determinantal and Pfaffian point processes. Specific tasks include computation of the Hausdorff dimension for the spectral measure of interval exchange maps (problem posed by Ya. Sinai), limit theorems for Hamiltonian flows on surfaces of higher genus (question of A. Katok), development of entropy theory and functional limit theorems for determinantal point processes and a description of the ergodic decomposition for infinite orthogonally-invariant measures on the space of infinite real matrices (the real case of the problem, posed in 2000 by A. Borodin and G. Olshanski, of harmonic analysis on the infinite-dimensional analogue of the Grassmann manifold). The project consolidates the proposer's past work, in particular, his limit theorems for translation flows (Annals of Math. 2014), his proof of the 1985 Vershik-Kerov entropy conjecture (GAFA 2012) and his solution of the complex case of the Borodin-Olshanski problem (preprint 2013). The proposer is currently PI of project ANR-11-IDEX-0001-02 (1.11.2013--30.10.2015; budget 360000 euro) under the Programme 'Investissements d'avenir' of the Government of the French Republic.'


year authors and title journal last update
List of publications.
2017 Ferenczi, S.; Kułaga-Przymus, J.; Lemańczyk, M.
Sarnak\'s Conjecture -- what\'s new
published pages: 65 pages, ISSN: , DOI: 1 2019-05-31
2018 Bufetov, Alexander I.; Solomyak, Boris
A spectral cocycle for substitution systems and translation flows
published pages: 11 pages, ISSN: , DOI:
arXiv:1802.04783 1 2019-05-31
2018 Alexander I. Bufetov, Yanqi Qiu
J-Hermitian determinantal point processes: balanced rigidity and balanced Palm equivalence
published pages: 127-188, ISSN: 0025-5831, DOI: 10.1007/s00208-017-1627-y
Mathematische Annalen 371/1-2 2019-05-31
2017 Alexander I. Bufetov, Yanqi Qiu
Conditional measures of generalized Ginibre point processes
published pages: 4671-4708, ISSN: 0022-1236, DOI: 10.1016/j.jfa.2017.03.004
Journal of Functional Analysis 272/11 2019-05-31
2016 Fan, Shilei; Liao, Lingmin
Rational map ax+1/x on the projective line over $mathbb{Q}_2$
published pages: 13 pages, ISSN: , DOI: 1 2019-05-31
2017 Alexander I. Bufetov, Yanqi Qiu
Determinantal Point Processes Associated with Hilbert Spaces of Holomorphic Functions
published pages: 1-44, ISSN: 0010-3616, DOI: 10.1007/s00220-017-2840-y
Communications in Mathematical Physics 351/1 2019-05-31
2017 Alexander Igorevich Bufetov, Tomoyuki Shirai
Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces
published pages: 1-5, ISSN: 0386-2194, DOI: 10.3792/pjaa.93.1
Proceedings of the Japan Academy, Series A, Mathematical Sciences 93/1 2019-05-31
2016 Bufetov, Alexander I.
Conditional measures of determinantal point processes
published pages: , ISSN: , DOI:
arXiv:1605.01400 1 2019-05-31
2018 Bufetov, Alexander I.; Dymov, Andrey V.; Osada, Hirofumi
The logarithmic derivative for point processes with equivalent Palm measures
published pages: 18 pages, ISSN: 0025-5645, DOI:
Journal Mathematical Society of Japan 1 2019-05-31
2017 Alexander I. Bufetov, Yanqi Qiu
Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields
published pages: 2482-2533, ISSN: 0010-437X, DOI: 10.1112/S0010437X17007412
Compositio Mathematica 153/12 2019-05-31
2016 A I Bufetov
Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. II. Convergence of infinite determinantal measures
published pages: 299-315, ISSN: 1064-5632, DOI: 10.1070/IM8384
Izvestiya: Mathematics 80/2 2019-05-31
2016 Bufetov, Alexander,; Qiu, Yanqi; Shamov, Alexander
Kernels of conditional determinantal measures
published pages: , ISSN: , DOI: 1 2019-05-31
2017 Bufetov, Alexander I.; Romanov, Roman V.
Division subspaces and integrable kernels
published pages: 11 pages, ISSN: , DOI: 1 2019-05-31
2017 Bergelson, Vitaly; Kułaga-Przymus, Joanna; Lemańczyk, Mariusz; Richter, Florian K.
A structure theorem for level sets of multiplicative functions and applications
published pages: 32 pages, ISSN: , DOI: 1 2019-05-31
2017 Alexander I. Bufetov, Boris Solomyak
On ergodic averages for parabolic product flows (Version 3)
published pages: 14, ISSN: , DOI:
arXiv:1612.09142 2019-05-31
2017 Alexander I. Bufetov
A palm hierarchy for determinantal point processes with the Bessel kernel
published pages: 90-97, ISSN: 0081-5438, DOI: 10.1134/s0081543817040058
Proceedings of the Steklov Institute of Mathematics 297/1 2019-05-31
2018 Alexander I. Bufetov, Shilei Fan, Yanqi Qiu
Equivalence of Palm measures for determinantal point processes governed by Bergman kernels
published pages: , ISSN: 0178-8051, DOI: 10.1007/s00440-017-0803-z
Probability Theory and Related Fields 2019-05-31
2017 Fan, Shilei; Qiu, Yanqi
Invariant measures for the actions of the modular group
published pages: 5 pages, ISSN: , DOI: 1 2019-05-31
2016 A I Bufetov
Infinite determinantal measures and the ergodic decomposition of infinite Pickrell measures. III. The infinite Bessel process as the limit of the radial parts of finite-dimensional projections of infinite Pickrell measures
published pages: 1035-1056, ISSN: 1064-5632, DOI: 10.1070/IM8385
Izvestiya: Mathematics 80/6 2019-05-31
2018 Nizar Demni, Pierre Lazag
The Hyperbolic-type Point Process
published pages: 12 pages, ISSN: , DOI:
arXiv:1712.04824 2019-05-31
2018 Alexander I Bufetov, Andrey V Dymov
A Functional Limit Theorem for the Sine-Process
published pages: , ISSN: 1073-7928, DOI: 10.1093/imrn/rny104
International Mathematics Research Notices 2019-05-31
2018 Alexander I. Bufetov, Roman V. Romanov
Division subspaces and integrable kernels
published pages: 11, ISSN: 0024-6093, DOI: 10.1112/blms.12223
Bulletin of the London Mathematical Society 2019-02-28
2018 Bufetov, Alexander I.; Qiu, Yanqi
Patterson-Sullivan measures for point processes and the reconstruction of harmonic functions
published pages: 57, ISSN: , DOI: 2019-02-28
2018 Bufetov, Alexander I.; Klimenko, Alexey; Series, Caroline
Convergence of spherical averages for actions of Fuchsian Groups
published pages: 56, ISSN: , DOI: 2019-02-28

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