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pro vyhledávání: '"Litvak, A. E."'
Autor:
Arman, Andrii, Litvak, Alexander E.
We improve some upper bounds for minimal dispersion on the cube and torus. /Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion in several previous works. Our new lemma combines a random and non-ra
Externí odkaz:
http://arxiv.org/abs/2406.02757
We provide the first useful and rigorous analysis of ensemble sampling for the stochastic linear bandit setting. In particular, we show that, under standard assumptions, for a $d$-dimensional stochastic linear bandit with an interaction horizon $T$,
Externí odkaz:
http://arxiv.org/abs/2311.08376
We study the volume ratio between projections of two convex bodies. Given a high-dimensional convex body $K$ we show that there is another convex body $L$ such that the volume ratio between any two projections of fixed rank of the bodies $K$ and $L$
Externí odkaz:
http://arxiv.org/abs/2211.06094
Autor:
Yang, Julia C., Bowling, David R., Smith, Kenneth R., Kunik, Lewis, Raczka, Brett, Anderegg, William R.L., Bahn, Michael, Blanken, Peter D., Richardson, Andrew D., Burns, Sean P., Bohrer, Gil, Desai, Ankur R., Arain, M. Altaf, Staebler, Ralf M., Ouimette, Andrew P., Munger, J. William, Litvak, Marcy E.
Publikováno v:
In Agricultural and Forest Meteorology 15 June 2024 353
We provide a new construction for a set of boxes approximating axis-parallel boxes of fixed volume in $[0, 1]^d$. This improves upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-perio
Externí odkaz:
http://arxiv.org/abs/2108.10374
Publikováno v:
In Journal of Functional Analysis 1 February 2024 286(3)
Publikováno v:
Zap. Nauchn. Sem. POMI, 505, POMI, 2021, 162-171
Consider some convex body $K\subset\mathbb R^d$. Let $X_1,\dots, X_k$, where $k\leq d$, be random points independently and uniformly chosen in $K$, and let $\xi_k$ be a uniformly distributed random linear $k$-plane. We show that for $p\geq-d+k+1$, \[
Externí odkaz:
http://arxiv.org/abs/2007.06743
Autor:
Litvak, A. E.
We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.
Comment: More typos are corrected. N
Comment: More typos are corrected. N
Externí odkaz:
http://arxiv.org/abs/2005.12243
Let $M_n$ be an $n\times n$ random matrix with i.i.d. Bernoulli(p) entries. We show that there is a universal constant $C\geq 1$ such that, whenever $p$ and $n$ satisfy $C\log n/n\leq p\leq C^{-1}$, \begin{align*} {\mathbb P}\big\{\mbox{$M_n$ is sing
Externí odkaz:
http://arxiv.org/abs/2004.03131
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