Zobrazeno 1 - 10
of 240
pro vyhledávání: '"Pegon, P."'
Autor:
Pegon, Paul, Petrache, Mircea
We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties arise, since
Externí odkaz:
http://arxiv.org/abs/2309.08677
Autor:
Nenna, Luca, Pegon, Paul
Publikováno v:
Canadian Journal of Mathematics, March 2024, First View, pp. 1-21
We investigate the convergence rate of multi-marginal optimal transport costs that are regularized with the Boltzmann-Shannon entropy, as the noise parameter $\varepsilon$ tends to $0$. We establish lower and upper bounds on the difference with the u
Externí odkaz:
http://arxiv.org/abs/2307.03023
In this paper, we establish a $C^{1,\alpha}$-regularity theorem for almost-minimizers of the functional $\mathcal{F}_{\varepsilon,\gamma}=P-\gamma P_{\varepsilon}$, where $\gamma\in(0,1)$ and $P_{\varepsilon}$ is a nonlocal energy converging to the p
Externí odkaz:
http://arxiv.org/abs/2209.11006
We investigate the convergence rate of the optimal entropic cost $v_\varepsilon$ to the optimal transport cost as the noise parameter $\varepsilon \downarrow 0$. We show that for a large class of cost functions $c$ on $\mathbb{R}^d\times \mathbb{R}^d
Externí odkaz:
http://arxiv.org/abs/2206.03347
Autor:
Monteil, Antonin, Pegon, Paul
Publikováno v:
Journal de l'\'Ecole polytechnique - Math\'ematiques, Tome 11 (2024), pp. 431-472
We consider first order local minimization problems of the form $\min \int_{\mathbb{R}^N}f(u,\nabla u)$ under a mass constraint $\int_{\mathbb{R}^N}u=m$. We prove that the minimal energy function $H(m)$ is always concave, and that relevant rescalings
Externí odkaz:
http://arxiv.org/abs/2203.01250
Motivated by some models of pattern formation involving an unoriented director field in the plane, we study a family of unoriented counterparts to the Aviles-Giga functional. We introduce a nonlinear curl operator for such unoriented vector fields as
Externí odkaz:
http://arxiv.org/abs/2112.04959
Autor:
Merlet, Benoit, Pegon, Marc
Publikováno v:
Journal de l'\'Ecole polytechnique -- Math\'ematiques 9 (2021), pp. 63-100
Motivated by Gamow's liquid drop model in the large mass regime, we consider an isoperimetric problem in which the standard perimeter $P(E)$ is replaced by $P(E)-\gamma P_\varepsilon(E)$, with $0<\gamma<1$ and $P_\varepsilon$ a nonlocal energy such t
Externí odkaz:
http://arxiv.org/abs/2106.02442
Autor:
Wright, Paul, White, Catherine, Parker, Ryan C., Pegon, Jean-Sébastien, Menchetti, Marco, Pearse, Joseph, Bahrami, Arash, Moroz, Anastasia, Wonfor, Adrian, Penty, Richard V., Spiller, Timothy P., Lord, Andrew
Publikováno v:
J. Opt. Commun. Netw. 13, 33-40 (2021)
We demonstrate how the 5G network slicing model can be extended to address data security requirements. In this work we demonstrate two different slice configurations, with different encryption requirements, representing two diverse use-cases for 5G n
Externí odkaz:
http://arxiv.org/abs/2007.03377
We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This is the Lagrangian counterpart of the recent Eulerian version proved in [CDM19a].
Externí odkaz:
http://arxiv.org/abs/2003.11793
Autor:
Pegon, Marc
This paper is concerned with volume-constrained minimization problems derived from Gamow's liquid drop model for the atomic nucleus, involving the competition of a perimeter term and repulsive nonlocal potentials. We consider a large class of potenti
Externí odkaz:
http://arxiv.org/abs/2003.01165