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pro vyhledávání: '"Raz, Orit"'
Autor:
Baer-Erenfeld, Hadas, Raz, Orit E.
Let $\gamma_1,\gamma_2$ be a pair of constant-degree irreducible algebraic curves in $\mathbb{R}^d$. Assume that $\gamma_i$ is neither contained in a hyperplane nor in a quadric surface in $\mathbb{R}^d$, for each $i=1,2$. We show that for every pair
Externí odkaz:
http://arxiv.org/abs/2304.06812
Jord\'an and Tanigawa recently introduced the $d$-dimensional algebraic connectivity $a_d(G)$ of a graph $G$. This is a quantitative measure of the $d$-dimensional rigidity of $G$ which generalizes the well-studied notion of spectral expansion of gra
Externí odkaz:
http://arxiv.org/abs/2304.01306
The $d$-dimensional algebraic connectivity $a_d(G)$ of a graph $G=(V,E)$, introduced by Jord\'an and Tanigawa, is a quantitative measure of the $d$-dimensional rigidity of $G$ that is defined in terms of the eigenvalues of stiffness matrices (which a
Externí odkaz:
http://arxiv.org/abs/2205.05530
We consider the Erd\H{o}s-R\'enyi evolution of random graphs, where a new uniformly distributed edge is added to the graph in every step. For every fixed $d\ge 1$, we show that with high probability, the graph becomes rigid in $\mathbb R^d$ at the ve
Externí odkaz:
http://arxiv.org/abs/2202.09917
Autor:
Raz, Orit E., Zahl, Joshua
Publikováno v:
Geom. Funct. Anal. 34, 209--262, 2024
We consider four related problems. (1) Obtaining dimension estimates for the set of exceptional vantage points for the pinned Falconer distance problem. (2) Nonlinear projection theorems, in the spirit of Kaufman, Bourgain, and Shmerkin. (3) The para
Externí odkaz:
http://arxiv.org/abs/2108.07311
We show that the maximum number of pairwise non-overlapping $k$-rich lenses (lenses formed by at least $k$ circles) in an arrangement of $n$ circles in the plane is $O\left(\frac{n^{3/2}\log{(n/k^3)}}{k^{5/2}} + \frac{n}{k} \right)$, and the sum of t
Externí odkaz:
http://arxiv.org/abs/2012.04204
Autor:
Raz, Orit E., Zahl, Joshua
We characterize when bivariate real analytic functions are "dimension expanding" when applied to a Cartesian product. If $P$ is a bivariate real analytic function that is not locally of the form $P(x,y) = h(a(x) + b(y))$, then whenever $A$ and $B$ ar
Externí odkaz:
http://arxiv.org/abs/2010.04845
Autor:
Raz, Orit E., Solymosi, József
While the problem of determining whether an embedding of a graph $G$ in $\mathbb{R}^2$ is {\it infinitesimally rigid} is well understood, specifying whether a given embedding of $G$ is {\it rigid} or not is still a hard task that usually requires ad
Externí odkaz:
http://arxiv.org/abs/1901.10631
Autor:
Raz, Orit E., Wigderson, Avi
This paper presents a deterministic, strongly polynomial time algorithm for computing the matrix rank for a class of symbolic matrices (whose entries are polynomials over a field). This class was introduced, in a different language, by Lov\'asz [Lov]
Externí odkaz:
http://arxiv.org/abs/1901.09423
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