Zobrazeno 1 - 10
of 140
pro vyhledávání: '"Poly , Guillaume"'
We characterize the limiting distributions of random variables of the form $P_n\left( (X_i)_{i \ge 1} \right)$, where: (i) $(P_n)_{n \ge 1}$ is a sequence of multivariate polynomials, each potentially involving countably many variables; (ii) there ex
Externí odkaz:
http://arxiv.org/abs/2412.06749
We consider random trigonometric polynomials with general dependent coefficients. We show that under mild hypotheses on the structure of dependence, the asymptotics as the degree goes to infinity of the expected number of real zeros coincides with th
Externí odkaz:
http://arxiv.org/abs/2409.15057
In this article, we revisit the question of fluctuations of linear statistics of beta ensembles in the single cut and non-critical regime for general potentials $V$ under mild regularity and growth assumptions. Our main objective is to establish shar
Externí odkaz:
http://arxiv.org/abs/2403.17211
We investigate the entropy $H(\mu,t)$ of a probability measure $\mu$ along the heat flow and more precisely we seek for closed algebraic representations of its derivatives. Provided that $\mu$ admits moments of any order, it is indeed proved in [Guo
Externí odkaz:
http://arxiv.org/abs/2311.04831
A total variation version of Breuer--Major Central Limit Theorem under $\mathbb{D}^{1,2}$ assumption
In this note, we establish a qualitative total variation version of Breuer--Major Central Limit Theorem for a sequence of the type $\frac{1}{\sqrt{n}} \sum_{1\leq k \leq n} f(X_k)$, where $(X_k)_{k\ge 1}$ is a centered stationary Gaussian process, un
Externí odkaz:
http://arxiv.org/abs/2309.06265
We study the regularity of the law of a quadratic form $Q(X,X)$, evaluated in a sequence $X = (X_{i})$ of independent and identically distributed random variables, when $X_{1}$ can be expressed as a sufficiently smooth function of a Gaussian field. T
Externí odkaz:
http://arxiv.org/abs/2303.09488
We establish an unexpected phenomenon of strong regularization along normal convergence on Wiener chaoses. For every sequence of chaotic random variables, convergence in law to the Gaussian distribution is upgraded to superconvergence: the regularity
Externí odkaz:
http://arxiv.org/abs/2303.02628
Let $(Z_k)_{k\geq 1}$ be a sequence of independent and identically distributed complex random variables with common distribution $\mu$ and let $P_n(X):=\prod_{k=1}^n (X-Z_k)$ the associated random polynomial in $\mathbb C[X]$. In [Kab15], the author
Externí odkaz:
http://arxiv.org/abs/2301.06973
We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of any triple
Externí odkaz:
http://arxiv.org/abs/2211.07314
Autor:
Angst, Jürgen, Poly, Guillaume
Let us consider i.i.d. random variables $\{a_k,b_k\}_{k \geq 1}$ defined on a common probability space $(\Omega, \mathcal F, \mathbb P)$, following a symmetric Rademacher distribution and the associated random trigonometric polynomials $S_n(\theta)=
Externí odkaz:
http://arxiv.org/abs/2111.12571