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pro vyhledávání: '"Chiclana, Rafael"'
In this paper we prove the existence of H\"{o}lder continuous terminal embeddings of any desired $X \subseteq \mathbb{R}^d$ into $\mathbb{R}^{m}$ with $m=\mathcal{O}(\varepsilon^{-2}\omega(S_X)^2)$, for arbitrarily small distortion $\varepsilon$, whe
Externí odkaz:
http://arxiv.org/abs/2408.02812
The celebrated Johnson-Lindenstrauss lemma states that for all $\varepsilon \in (0,1)$ and finite sets $X \subseteq \mathbb{R}^N$ with $n>1$ elements, there exists a matrix $\Phi \in \mathbb{R}^{m \times N}$ with $m=\mathcal{O}(\varepsilon^{-2}\log n
Externí odkaz:
http://arxiv.org/abs/2403.03969
Autor:
Chiclana, Rafael, Peres, Yuval
We study hitting times in simple random walks on graphs, which measure the time required to reach specific target vertices. Our main result establishes a sharp lower bound for the variance of hitting times. For a simple random walk on a graph with $n
Externí odkaz:
http://arxiv.org/abs/2312.07726
Autor:
Chiclana, Rafael, Peres, Yuval
There is a long history of establishing central limit theorems for Markov chains. Quantitative bounds for chains with a spectral gap were proved by Mann and refined later. Recently, rates of convergence for the total variation distance were obtained
Externí odkaz:
http://arxiv.org/abs/2212.00958
Autor:
Chiclana, Rafael
We characterize the functions $f\colon [0,1] \longrightarrow [0,1]$ for which there exists a measurable set $C\subseteq [0,1]$ of positive measure satisfying $\frac{|C\cap I|}{|I|}
Externí odkaz:
http://arxiv.org/abs/2108.02663
Autor:
Chiclana, Rafael, Peres, Yuval
We show that for lazy simple random walks on finite spherically symmetric trees, the ratio of the mixing time and the relaxation time is bounded by a universal constant. Consequently, lazy simple random walks on any sequence of finite spherically sym
Externí odkaz:
http://arxiv.org/abs/2107.14111
Autor:
Chiclana, Rafael, Martin, Miguel
We study the stability behavior of the Bishop-Phelps-Bollob\'as property for Lipschitz maps (Lip-BPB property). This property is a Lipschitz version of the classical Bishop-Phelps-Bollob\'as property and deals with the possibility of approximating a
Externí odkaz:
http://arxiv.org/abs/2004.10649
Akademický článek
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We study the density of the set $\operatorname{SNA}(M,Y)$ of those Lipschitz maps from a (complete pointed) metric space $M$ to a Banach space $Y$ which strongly attain their norm (i.e.\ the supremum defining the Lipschitz norm is actually a maximum)
Externí odkaz:
http://arxiv.org/abs/1907.07698
Autor:
Chiclana, Rafael, Martin, Miguel
Publikováno v:
Nonlinear Analysis 188 (2019), 158--178
In this paper, we introduce and study a Lipschitz version of the Bishop-Phelps-Bollob\'as property (Lip-BPB property). This property deals with the possibility of making a uniformly simultaneous approximation of a Lipschitz map $F$ and a pair of poin
Externí odkaz:
http://arxiv.org/abs/1901.02956