Preprint:
(2024) Roots of random trigonometric polynomials with general dependent coefficients, J.Angst, O.Nguyen, G.Poly
(2024) Sharp total variation rates of convergence for fluctuations of linear statistics of β-ensembles, J.Angst, R.Herry, D.Malicet and G.Poly.
Accepted articles:
(2024) A contribution to the MMSE conjecture, P.Mansanarez, G.Poly and Y.Swan, to appear in IEEE.
(2024) On the regularity of densities of quadratic forms in random variables, R.Herry, D.Malicet and G.Poly, to appear in Probability Theory and Related Fields.
(2023) A total variation version of Breuer--Major Central Limit Theorem under the D^{1,2} assumption, J.Angst, F.Dalmao and G.Poly, to appear in Electronic Communications in Probability.
(2023) Random zonal eigenfunctions and H¨older version of the Paley-Zygmund theorem on compact manifolds, P.Brun, R.Imekraz and G.Poly, to appear in Bulletin de la SMF.
(2023) Central convergence on Wiener chaoses always implies asymptotic smoothness and C-infinite convergence of densities, R.Herry, D.Malicet and G.Poly, to appear in Annals of Probability.
(2023) Almost sure convergence of the empirical measure of roots of derivatives of polynomials with independent random roots, J.Angst, D.Malicet and G.Poly, to appear in Bulletin of the London Mathematical society.
(2022) A short proof of the strong three dimensional Gaussian product inequality, R.Herry, D.Malicet and G.Poly, to appear in Proceedings of the American Mathematical Society.
(2022) Fluctuation on Salem-Zygmund central limit Theorem, Electron. J. Probab. 28: 1-40 (2023).
(2022) Real zeros of random trigonometric polynomials with dependent coefficients, J.Angst, T.Pautrel and G.Poly, to appear in Transactions of American Mathematical Society.
(2022) On the zeros of non-analytic random periodic signals, J.Angst and G.Poly. International Mathematics Research Notices, Volume 2022, Issue 7.
(2021) Variations on Salem–Zygmund results for random trigonometric polynomials, J.Angst and G.Poly. Electron. J. Probab. 26: 1-36.
(2020) Regularization lemmas and convergence in total variation, V. Bally, L. Caramellino and G. Poly. Electron. J. Probab. 25: 1-20.
(2020) On the absolute continuity of random nodal volumes, J. Angst and G. Poly, Ann. Probab. 48(5): 2145-2175 .
(2019) Almost sure convergence on chaoses, G. Zheng and G. Poly. Proc. Amer. Math. Soc. 147 (2019), 4055-4065.
(2019) Non universality for the variance of the number of real roots of random trigonometric polynomials,V. Bally, Lucia Caramellino, G. Poly, Probability Theory and Related Fields 174, pages 887–927.
(2018) Stein characterizations for linear combinations of gamma random variables, Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly and Yvik Swan, to appear in Brazilian Journal of Probability and Statistics.
(2018) Convergence in distribution norms in the CLT for non identical distributed random variables, V. Bally, Lucia Caramellino, G. Poly. Electronic Journal of Probability, Volume 23, paper n°45, 51 pp.
(2018) On the real zeros of random trigonometric polynomials with dependent coefficients, J. Angst, F. Dalmao, G. Poly. Proceedings of the American Mathematical Society, Vol 147 , 205-214.
(2018) Stein's method on the second Wiener chaos: 2-Wasserstein distance, B. Arras, E. Azmoodeh, G. Poly and Y. Swan. Stochastic Processes and their Applications.
(2018) Universality of the nodal length of bivariate random trigonometric polynomials, J. Angst, G. Poly. Transactions of American Mathematical Society,
(2017) A weak Cramèr condition and application to Edgeworth's expansions, J. Angst, G. Poly. Electronic Journal of Probability, vol. 22, paper n°59, 24 pp.
(2016) Generalization of the Nualart-Peccati criterion, E.Azmoodeh, D.Malicet, G.Mijoule and G.Poly, Annals of Probability, Volume 44, Number 2.
(2015) Multidimensional limit theorems for homogeneous sums: a general transfer principle, I.Nourdin, G.Peccati, G.Poly and R.Simone. ESAIM, vol 20, p 293--308.
(2015) Multivariate Gaussian approximations on Markov chaoses, S. Campese, I. Nourdin, G. Peccati and G. Poly. Electronic communications in Probability, vol. 21, paper n°48, 9 pp.
(2015) Squared chaotic random variables: new moment inequalities with applications, D. Malicet, I. Nourdin, G. Peccati and G. Poly. Journal of Functional Analysis, vol. 270, 2016, Pages 649-670.
(2014) The law of the iterated logarithm for subordinated Gaussian sequences: uniform Wasserstein bounds, E. Azmoodeh, G. Peccati and G. Poly.
ALEA, Lat. Am. J. Probab. Math. Stat. 13, 659–686
(2014) An invariance principle under the total variation distance, I.Nourdin and G.Poly, Stochastic processes and their applications, 2015, vol. 125, issue 6, pages 2190-2205
(2014) Classical and free Fourth Moment Theorems: universality and thresholds, I.Nourdin, G.Peccati, G.Poly and R.Simone. To appear in Journal of Theoretical Probability.
(2014) Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach. E.Azmoodeh, G.Peccati and G.Poly. In Memoriam Marc Yor - Séminaire de Probabilités XLVII, Volume 2137 of the series Lecture Notes in Mathematics pp 339-367.
(2013) Two properties of vectors of quadratic forms in Gaussian random variables, V.I.Bogachev, E.D.Kosov, I.Nourdin and G.Poly. Theory of Probability and its Applications. 2014, Volume 59, Issue 2, Pages 214–232.
(2013) Properties of convergence in Dirichlet structures, D.Malicet and G.Poly, Journal of Functional Analysis, Vol 9, 2077-2096.
(2013) Fourth moment theorems for Markov diffusion generators, E.Azmoodeh, S.Campese and G.Poly, Journal of Functional Analysis, Volume 266, Issue 4.
(2013) Absolute continuity and convergence of densities for random vectors on Wiener chaos, I.Nourdin, D.Nualart and G.Poly, Electronic Journal of Probability, Vol 18, no 22.
(2013) Convergence in total variation on Wiener chaos, I.Nourdin and G.Poly, Stochastic Processes and Applications, 123, no 2, 651-674
(2012) Convergence in law in the second Wiener/Wigner chaos, I.Nourdin and G.Poly, Electronic Communications in Probability, 17, no 36
Proceedings of conferences:
(2014) Stein's method, Malliavin calculus, Dirichlet forms and the fourth momentTheorem, L.H.Y. Chen and G.Poly. Festschrift Masatoshi Fukushima (Z-Q Chen, N. Jacob, M. Takeda and T. Uemura, eds.), Interdisciplinary Mathematical Sciences Vol. 17, World Scientific 2015, 107-130
(2013) Convergence in law implies convergence in total variation for polynomials in independent Gaussian, Gamma or Beta random variables, I.Nourdin and G.Poly. (to appear in proceedings of the High Dimensional Probability VII meeting)
Non published notes/ unsubmitted articles:
(2013) Absolute continuity of Markov chains ergodic measures by Dirichlet forms methods, G.Poly, (ongoing research to get criteria of smoothness of ergodic measures of Markov chains)
(2019) Regularization along central convergence on second and third Wiener chaoses, G. Poly.
(2016) A new approach to the Stein-Tikhomirov method: with applications to the second Wiener chaos and Dickman convergence, B. Arras, G. Mijoule, G. Poly and Y. Swan.
(2015) Universality of the mean number of real zeros of random trigonometric polynomials under a weak Cramer condition, J. Angst and G. Poly.
(2015) Local universality of the number of zeros of random trigonometric polynomials with continuous coefficients, J.M Azais, F. Dalmao, J.R. Léon, I. Nourdin and G. Poly.
PHD Thesis: Dirichlet forms and applications to the ergodic theory of Markov chains
(under the supervision of Nicolas Bouleau)
This thesis explored the consequence of the so-called energy image density (E.I.D.) in various problems arising in ergodic theory of Markov chains. The E.I.D. property is conjectured true for any general Dirichlet form admitting a square field operator and holds for the natural Dirichlet forms arising in stochastic calculus (such that the Ornstein-Uhlenbeck Dirichlet form). Roughly speaking, it provides a criterion of absolute continuity with respect to the Lebesgue measure for some random vectors whose components lie in the domain of the form. In the thesis was developed a reinforcement of the E.I.D. property yielding to new results in the direction of the Bouleau-Hirsch conjecture.
This thesis led to the papers "Properties of convergence in Dirichlet structures" and "Absolute continuity of Markov chains ergodic measures by Dirichlet forms methods".