Zobrazeno 1 - 10
of 167
pro vyhledávání: '"Ren, Kevin"'
Autor:
Orponen, Tuomas, Ren, Kevin
We show that the "sharp Kaufman projection theorem" from 2023 is sharp in the class of Ahlfors $(1,\delta^{-\epsilon})$-regular sets. This is in contrast with a recent result of the first author, which improves the projection theorem in the class of
Externí odkaz:
http://arxiv.org/abs/2411.04528
We prove that if $(\mathcal{M},d)$ is an $n$-point metric space that embeds quasisymmetrically into a Hilbert space, then for every $\tau>0$ there is a random subset $\mathcal{Z}$ of $\mathcal{M}$ such that for any pair of points $x,y\in \mathcal{M}$
Externí odkaz:
http://arxiv.org/abs/2410.21931
Autor:
Veerapaneni, Rishi, Jakobsson, Arthur, Ren, Kevin, Kim, Samuel, Li, Jiaoyang, Likhachev, Maxim
Multi-Agent Path Finding (MAPF) is the problem of effectively finding efficient collision-free paths for a group of agents in a shared workspace. The MAPF community has largely focused on developing high-performance heuristic search methods. Recently
Externí odkaz:
http://arxiv.org/abs/2409.14491
Distribution shift is a key challenge for predictive models in practice, creating the need to identify potentially harmful shifts in advance of deployment. Existing work typically defines these worst-case shifts as ones that most degrade the individu
Externí odkaz:
http://arxiv.org/abs/2407.03557
We generalize the recent results on radial projections by Orponen, Shmerkin, Wang using two different methods. In particular, we show that given $X,Y\subset \mathbb{R}^n$ Borel sets and $X\neq \emptyset$. If $\dim Y \in (k,k+1]$ for some $k\in \{1,\d
Externí odkaz:
http://arxiv.org/abs/2406.09707
Autor:
Veerapaneni, Rishi, Wang, Qian, Ren, Kevin, Jakobsson, Arthur, Li, Jiaoyang, Likhachev, Maxim
Multi-agent path finding (MAPF) is the problem of finding collision-free paths for a team of agents to reach their goal locations. State-of-the-art classical MAPF solvers typically employ heuristic search to find solutions for hundreds of agents but
Externí odkaz:
http://arxiv.org/abs/2403.20300
In this paper, we establish the existence of a bounded, linear extension operator $T: L^{2,p}(E) \to L^{2,p}(\mathbb{R}^2)$ when $1
Externí odkaz:
http://arxiv.org/abs/2402.11731
We prove some weighted refined decoupling estimates. As an application, we give an alternative proof of the following result on Falconer's distance set problem by the authors in a companion work: if a compact set $E\subset \mathbb{R}^d$ has Hausdorff
Externí odkaz:
http://arxiv.org/abs/2309.04501
We show that if a compact set $E\subset \mathbb{R}^d$ has Hausdorff dimension larger than $\frac{d}{2}+\frac{1}{4}-\frac{1}{8d+4}$, where $d\geq 3$, then there is a point $x\in E$ such that the pinned distance set $\Delta_x(E)$ has positive Lebesgue
Externí odkaz:
http://arxiv.org/abs/2309.04103
Autor:
Ren, Kevin
We generalize a Furstenberg-type result of Orponen-Shmerkin to higher dimensions, leading to an $\epsilon$-improvement in Kaufman's projection theorem for hyperplanes and an unconditional discretized radial projection theorem in the spirit of Orponen
Externí odkaz:
http://arxiv.org/abs/2309.04097