On the absolute continuity of random nodal volumes

Autor: Guillaume Poly, Jürgen Angst

Publikováno v: Annals of Probability
Annals of Probability, 2020, 48 (5), pp.2145-2175. ⟨10.1214/19-AOP1418⟩
Ann. Probab. 48, no. 5 (2020), 2145-2175
Annals of Probability, Institute of Mathematical Statistics, 2020, 48 (5), pp.2145-2175. ⟨10.1214/19-AOP1418⟩

International audience; We study the absolute continuity with respect to the Lebesgue measure of the distribution of the nodal volume associated with a smooth, non-degenerated and stationary Gaussian field $(f(x), {x \in \mathbb R^d})$. Under mild co

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d2a3cc4ee31109e4d852982779d37a40
https://hal.science/hal-02359411

ALMOST SURE CONVERGENCE ON CHAOSES

Autor: Guillaume Poly, Guangqu Zheng

Publikováno v: Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society, American Mathematical Society, 2019, 147 (9), pp.4055-4065. ⟨10.1090/proc/14557⟩
Proceedings of the American Mathematical Society, 2019, 147 (9), pp.4055-4065. ⟨10.1090/proc/14557⟩

We present several new phenomena about almost sure convergence on homogeneous chaoses that include Gaussian Wiener chaos and homogeneous sums in independent random variables. Concretely, we establish the fact that almost sure convergence on a fixed f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e6df21ea1700e42910ac10c063721a78
https://hal.archives-ouvertes.fr/hal-01987898

Convergence in distribution norms in the CLT for non identical distributed random variables

Autor: Lucia Caramellino, Vlad Bally, Guillaume Poly

Publikováno v: Electronic Journal of Probability
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2018, 23, paper 45, 51 p. ⟨10.1214/18-EJP174⟩
Electron. J. Probab.
Electronic Journal of Probability, 2018, 23, paper 45, 51 p. ⟨10.1214/18-EJP174⟩

We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is \[ \varepsilon _{n}(f):={\mathbb{E} }\Big (f\Big (\frac 1{\sqrt n}\sum _{i=1}^{n}Z_{i}\Big )\Big )-{\mathbb{E} }\big (f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::19b44959367bbea786f8c2b2f9c3adfd
https://hal-upec-upem.archives-ouvertes.fr/hal-01413548

A bound on the 2-Wasserstein distance between linear combinations of independent random variables

Autor: Ehsan Azmoodeh, Guillaume Poly, Yvik Swan, Benjamin Arras

Publikováno v: Stochastic processes and their applications, 129 (7
2017-41. This preprint corresponds to the third section of https://arxiv.org/abs/1601.03301. The main resu.. 2017
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Stochastic Processes and their Applications
Stochastic Processes and their Applications, 2019, 129 (7), pp.2341-2375. ⟨10.1016/j.spa.2018.07.009⟩

We provide a bound on a natural distance between finitely and infinitely supported elements of the unit sphere of $\ell^2(\mathbb{N}^*)$, the space of real valued sequences with finite $\ell^2$ norm. We use this bound to estimate the 2-Wasserstein di

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bb7416a3660acf58e550338e137b3f7e
https://hal.archives-ouvertes.fr/hal-01503225

A weak Cramér condition and application to Edgeworth expansions

Autor: Guillaume Poly, Jürgen Angst

Publikováno v: Electronic Journal of Probability
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2017, 22 (article 59), pp.1-24. 〈10.1214/17-EJP77〉
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2017, 22 (article 59), pp.1-24. ⟨10.1214/17-EJP77⟩
Electronic Journal of Probability, 2017, 22 (article 59), pp.1-24. ⟨10.1214/17-EJP77⟩
Electron. J. Probab.

International audience; We introduce a new, weak Cramer condition on the characteristic function of a random vector which does not only hold for all continuous distributions but also for discrete (non-lattice) ones in a generic sense. We then prove t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5af2a6077fe85cd64c629571acf3894
https://doi.org/10.1214/17-ejp77