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pro vyhledávání: '"Parraud, Félix"'
Autor:
Parraud, Félix
We consider operator-valued polynomials in Gaussian Unitary Ensemble random matrices and we show that its $L^p$-norm can be upper bounded, up to an asymptotically small error, by the operator norm of the same polynomial evaluated in free semicircular
Externí odkaz:
http://arxiv.org/abs/2410.04481
Autor:
Parraud, Félix, Schnelli, Kevin
In this paper we study multi-matrix models whose potentials are small perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of polynomials
Externí odkaz:
http://arxiv.org/abs/2310.12948
Autor:
Parraud, Félix
Let $U^N$ be a family of $N\times N$ independent Haar unitary random matrices and their adjoints, $Z^N$ a family of deterministic matrices, $P$ a self-adjoint noncommutative polynomial, i.e. such that for any $N$, $P(U^N,Z^N)$ is self-adjoint, $f$ a
Externí odkaz:
http://arxiv.org/abs/2302.02943
Autor:
PARRAUD, Félix
甲第23449号
理博第4743号
新制||理||1680(附属図書館)
(主査)教授 COLLINS Benoit Vincent Pierre, 教授 泉 正己, 教授 日野 正訓
学位規則第4条第1項該当
Doctor of Science
Kyoto University
理博第4743号
新制||理||1680(附属図書館)
(主査)教授 COLLINS Benoit Vincent Pierre, 教授 泉 正己, 教授 日野 正訓
学位規則第4条第1項該当
Doctor of Science
Kyoto University
Externí odkaz:
http://hdl.handle.net/2433/265977
Autor:
Parraud, Félix, Schnelli, Kevin
We study products of functions evaluated at self-adjoint polynomials in deterministic matrices and independent Wigner matrices; we compute the deterministic approximations of such products and control the fluctuations. We focus on minimizing the assu
Externí odkaz:
http://arxiv.org/abs/2208.02118
Autor:
Parraud, Félix, Schnelli, Kevin
Publikováno v:
In Linear Algebra and Its Applications 15 October 2024 699:1-46
Publikováno v:
Mathematische Annalen (2022), 1--32
One of the main applications of free probability is to show that for appropriately chosen independent copies of $d$ random matrix models, any noncommutative polynomial in these $d$ variables has a spectral distribution that converges asymptotically a
Externí odkaz:
http://arxiv.org/abs/2103.05962
Autor:
Collins, Benoît, Parraud, Félix
Publikováno v:
Journal of Mathematical Physics (2022) 63, no. 10, 102202
Given a random subspace $H_n$ chosen uniformly in a tensor product of Hilbert spaces $V_n\otimes W$, we consider the collection $K_n$ of all singular values of all norm one elements of $H_n$ with respect to the tensor structure. A law of large number
Externí odkaz:
http://arxiv.org/abs/2012.00159
Autor:
Parraud, Felix
Let $X^N$ be a family of $N\times N$ independent GUE random matrices, $Z^N$ a family of deterministic matrices, $P$ a self-adjoint non-commutative polynomial, that is for any $N$, $P(X^N)$ is self-adjoint, $f$ a smooth function. We prove that for any
Externí odkaz:
http://arxiv.org/abs/2011.04146
Autor:
Parraud, Félix
Let $U^N = (U_1^N,\dots, U^N_p)$ be a d-tuple of $N\times N$ independent Haar unitary matrices and $Z^{NM}$ be any family of deterministic matrices in $\mathbb{M}_N(\mathbb{C})\otimes \mathbb{M}_M(\mathbb{C})$. Let $P$ be a self-adjoint non-commutati
Externí odkaz:
http://arxiv.org/abs/2005.13834