Zobrazeno 1 - 10
of 365
pro vyhledávání: '"46B09"'
Let $\mathbb{B}_p^N$ be the $N$-dimensional unit ball corresponding to the $\ell_p$-norm. For each $N\in\mathbb N$ we sample a uniform random subspace $E_N$ of fixed dimension $m\in\mathbb{N}$ and consider the volume of $\mathbb{B}_p^N$ projected ont
Externí odkaz:
http://arxiv.org/abs/2412.16054
Autor:
Gordin, Miriam
We present vector-valued concentration inequalities for the biased measure on the discrete hypercube with an optimal dependence on the bias parameter and the Rademacher type of the target Banach space. These results allow us to obtain novel vector-va
Externí odkaz:
http://arxiv.org/abs/2410.09607
Autor:
Kadets, V., Zavarzina, O.
The Strong Law of Large Numbers (SLLN) for random variables or random vectors with different mathematical expectations easily reduces by means of shifts to SLLN for random variables or random vectors whose mathematical expectations are equal to zero.
Externí odkaz:
http://arxiv.org/abs/2410.04832
Autor:
Lee, Dong Neuck, Kosorok, Michael R.
Conventional off-policy reinforcement learning (RL) focuses on maximizing the expected return of scalar rewards. Distributional RL (DRL), in contrast, studies the distribution of returns with the distributional Bellman operator in a Euclidean space,
Externí odkaz:
http://arxiv.org/abs/2408.07660
Autor:
Astashkin, Sergey V.
We study subspaces of Orlicz spaces $L_M$ spanned by independent copies $f_k$, $k=1,2,\dots$, of a function $f\in L_M$, $\int_0^1 f(t)\,dt=0$. Any such a subspace $H$ is isomorphic to some Orlicz sequence space $\ell_\psi$. In terms of dilations of t
Externí odkaz:
http://arxiv.org/abs/2407.14870
An isoperimetric inequality on the Hamming cube for exponents $\beta\ge 0.50057$ is proved, achieving equality on any subcube. This was previously known for $\beta\ge \log_2(3/2)\approx 0.585$. Improved bounds are also obtained at the critical expone
Externí odkaz:
http://arxiv.org/abs/2407.12674
The real anisotropic Littlewood's $4 / 3$ inequality is an extension of a famous result obtained in 1930 by J. E. Littlewood. It asserts that, for $a , b \in ( 0 , \infty )$, the following conditions are equivalent: $\bullet$ There is an optimal cons
Externí odkaz:
http://arxiv.org/abs/2407.06804
Autor:
Allu, Vasudevarao, Pal, Subhadip
In this paper, we study a more general version of multidimensional Bohr radii for the holomorphic functions defined on unit ball of $\ell^n_q\,\,(1\leq q\leq \infty)$ spaces with values in arbitrary complex Banach spaces. More precisely, we study the
Externí odkaz:
http://arxiv.org/abs/2406.19865
Autor:
van Neerven, Jan, Riedle, Markus
We establish an explicit characterisation of L\'evy measures on both $L^p$-spaces and UMD Banach spaces. In the case of $L^p$-spaces, L\'evy measures are characterised by an integrability condition, which directly generalises the known description of
Externí odkaz:
http://arxiv.org/abs/2406.09362
Autor:
Ramanan, Kavita, Xie, Xiaoyu
Given an $n\times n$ matrix $A_n$ and $1\leq r, p \leq\infty$, consider the following quadratic optimization problem referred to as the $\ell_r$-Grothendieck problem: \begin{align}M_r(A_n)\coloneqq\max_{\boldsymbol{x}\in\mathbb{R}^n:\|\boldsymbol{x}\
Externí odkaz:
http://arxiv.org/abs/2404.18299