Zobrazeno 1 - 10
of 185
pro vyhledávání: '"van Handel, Ramon"'
The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general Gaussian (as well as non-Gaussian) random matrices in terms of an associated noncom
Externí odkaz:
http://arxiv.org/abs/2406.11453
A family of random matrices $\boldsymbol{X}^N=(X_1^N,\ldots,X_d^N)$ converges strongly to a family $\boldsymbol{x}=(x_1,\ldots,x_d)$ in a $C^*$-algebra if $\|P(\boldsymbol{X}^N)\|\to\|P(\boldsymbol{x})\|$ for every noncommutative polynomial $P$. This
Externí odkaz:
http://arxiv.org/abs/2405.16026
We prove nonasymptotic matrix concentration inequalities for the spectral norm of (sub)gaussian random matrices with centered independent entries that capture fluctuations at the Tracy-Widom scale. This considerably improves previous bounds in this s
Externí odkaz:
http://arxiv.org/abs/2401.06284
A classical result of Kahn and Saks states that given any partially ordered set with two distinguished elements, the number of linear extensions in which the ranks of the distinguished elements differ by $k$ is log-concave as a function of $k$. The l
Externí odkaz:
http://arxiv.org/abs/2309.13434
Autor:
Shou, Laura, van Handel, Ramon
We consider $N\times N$ self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with $d$ nonzero entries per row. We show that such random matrices exhibit a canonical localization-delocalization transition near t
Externí odkaz:
http://arxiv.org/abs/2307.16011
Autor:
van Handel, Ramon
The aim of this note is to show that the local form of the logarithmic Brunn-Minkowski conjecture holds for zonoids. The proof uses a variant of the Bochner method due to Shenfeld and the author.
Comment: 20 pages, final version
Comment: 20 pages, final version
Externí odkaz:
http://arxiv.org/abs/2202.09429
We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields sharp matrix c
Externí odkaz:
http://arxiv.org/abs/2201.05142
Publikováno v:
In Advances in Mathematics November 2024 456
Autor:
van Handel, Ramon
A well-known family of determinantal inequalities for mixed volumes of convex bodies were derived by Shephard from the Alexandrov-Fenchel inequality. The classic monograph Geometric Inequalities by Burago and Zalgaller states a conjecture on the vali
Externí odkaz:
http://arxiv.org/abs/2109.05169
Publikováno v:
Invent. Math. 234, 419-487 (2023)
A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian random matrices $X=\sum_i g_i A_i$ where $g_i$ are independent standard Gau
Externí odkaz:
http://arxiv.org/abs/2108.06312