Zobrazeno 1 - 10
of 94
pro vyhledávání: '"Marzo, Jordi"'
Publikováno v:
International Mathematics Research Notices, Vol. 2024, Issue 19, p. 12869-12903
We study the asymptotic behavior of the fluctuations of smooth and rough linear statistics for determinantal point processes on the sphere and on the Euclidean space. The main tool is the generalization of some norm representation results for functio
Externí odkaz:
http://arxiv.org/abs/2311.03204
Autor:
De La Torre, Víctor, Marzo, Jordi
A sequence $(X_N ) \subset \mathbb S^d$ of N-point sets from the d-dimensional sphere has QMC strength $s^*>d/2$ if it has worst-case error of optimal order, $N^{s/d}$, for Sobolev spaces of order $s$ for all $d/2 < s < s^*$ , and the order is not op
Externí odkaz:
http://arxiv.org/abs/2302.01001
Autor:
de la Torre, Victor, Marzo, Jordi
In 2011, Armentano, Beltr\'an and Shub obtained in \cite{ABS11} a closed expression for the expected logarithmic energy of the random point process on the sphere given by the roots of random elliptic polynomials. We consider a different approach whic
Externí odkaz:
http://arxiv.org/abs/2211.07599
Publikováno v:
Comput. Methods Funct. Theory 21 (2021), no. 4, 831-849
Let $\Omega$ be a convex open set in $\mathbb R^n$ and let $\Lambda_k$ be a finite subset of $\Omega$. We find necessary geometric conditions for $\Lambda_k$ to be interpolating for the space of multivariate polynomials of degree at most $k$. Our res
Externí odkaz:
http://arxiv.org/abs/2101.08064
Autor:
Marzo, Jordi, Mas, Albert
We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz $s$-energy on the sphere $\mathbb S^d.$ Our results are based in bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished manuscript whe
Externí odkaz:
http://arxiv.org/abs/1907.04814
Publikováno v:
J. Amer. Math. Soc. 34 (2021), 219-244
We find an explicit sequence of univariate polynomials of arbitrary degree with optimal condition number. This solves a problem posed by Michael Shub and Stephen Smale in 1993.
Externí odkaz:
http://arxiv.org/abs/1903.01356
Akademický článek
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Publikováno v:
J. Monatsh Math (2018) Vol. 186 , Issue 2, pp 235-248
We find t-designs on compact algebraic manifolds with a number of points comparable to the dimension of the space of polynomials of degree t on the manifold. This generalizes results on the sphere by Bondarenko, Radchenko and Viazovska. Of special in
Externí odkaz:
http://arxiv.org/abs/1612.06729
Autor:
Marzo, Jordi, Ortega-Cerdà, Joaquim
Publikováno v:
Constructive Approximation February 2018, Volume 47, Issue 1, pp 75-88
We compute the expected Riesz energy of random points on flat tori drawn from certain translation invariant determinantal processes and determine the process in the family providing the optimal asymptotic expected Riesz energy.
Externí odkaz:
http://arxiv.org/abs/1611.07667
Publikováno v:
Journal of Complexity 37, (2016) p. 76-109
We study expected Riesz s-energies and linear statistics of some determinantal processes on the sphere. In particular, we compute the expected Riesz and logarithmic energies of the determinantal processes given by the reproducing kernel of the space
Externí odkaz:
http://arxiv.org/abs/1511.02535