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157 results on '"Laurent Decreusefond"'

1. Optimal transport between determinantal point processes and application to fast simulation

Author

Laurent Decreusefond and Guillaume Moroz

Subjects
Applied mathematics. Quantitative methods, T57-57.97, Mathematics, QA1-939
Abstract

Two optimal transport problems between determinantal point processes (DPP for short) are investigated. It is shown how to estimate the Kantorovitch–Rubinstein and Wasserstein-2 distances between distributions of DPP. These results are applied to evaluate the accuracy of a fast but approximate simulation algorithm of the Ginibre point process restricted to a circle. One can now simulate in a reasonable amount of time more than ten thousands points.

Published
2021
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40. Wiener Space

Author

Laurent Decreusefond

Published
2022

44. Wiener Chaos

Author

Laurent Decreusefond

Published
2022

45. A User Centric Blockage Model for Wireless Networks

Author

Francois Baccelli, Bin Liu, Laurent Decreusefond, Rongfang Song, Dynamics of Geometric Networks (DYOGENE), Département d'informatique - ENS Paris (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), Département Informatique et Réseaux (INFRES), Télécom ParisTech, Nanjing University of Posts and Telecommunications [Nanjing] (NJUPT), Institut Polytechnique de Paris (IP Paris), Réseaux, Mobilité et Services (RMS), Laboratoire Traitement et Communication de l'Information (LTCI), Institut Mines-Télécom [Paris] (IMT)-Télécom Paris-Institut Mines-Télécom [Paris] (IMT)-Télécom Paris, and European Project: 788851,ERC,ERC-2017-ADG ,NEMO(2019)

Subjects
Networking and Internet Architecture (cs.NI), FOS: Computer and information sciences, Computer Science - Information Theory, Applied Mathematics, Information Theory (cs.IT), Quantitative Biology::Tissues and Organs, Coverage probability, Computer Science Applications, Computer Science - Networking and Internet Architecture, Best beam selection, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], C.2.0, [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT], Blockage, Beamforming, Iterative algorithm, Stochastic geometry, Multiplicative cascade, Electrical and Electronic Engineering
Abstract

International audience; This paper proposes a cascade blockage model for analyzing the vision that a user has of a wireless network. This model, inspired by the classical multiplicative cascade models, has a radial structure meant to analyze blockages seen by the receiver at the origin in different angular sectors. The main novelty is that it is based on the geometry of obstacles and takes the joint blockage phenomenon into account. We show on a couple of simple instances that the Laplace transforms of total interference satisfies a functional equation that can be solved efficiently by an iterative scheme. This is used to analyze the coverage probability of the receiver and the effect of blockage correlation and penetration loss in both dense and sparse blockage environments. Furthermore, this model is used to investigate the effect of blockage correlation on user beamforming techniques. Another functional equation and its associated iterative algorithm are proposed to derive the coverage performance of the best beam selection in this context. In addition, the conditional coverage probability is also derived to evaluate the effect of beam switching. The results not only show that beam selection is quite efficient for multi-beam terminals, but also show how the correlation brought by blockages can be leveraged to accelerate beam sweeping and pairing.

Published
2022

49. Stein’s Method for Rough Paths

Author

Laurent Decreusefond, Laure Coutin, Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Télécom ParisTech, Data, Intelligence and Graphs (DIG), Laboratoire Traitement et Communication de l'Information (LTCI), Institut Mines-Télécom [Paris] (IMT)-Télécom Paris-Institut Mines-Télécom [Paris] (IMT)-Télécom Paris, Département Informatique et Réseaux (INFRES), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), and Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Stein method, Probability (math.PR), 010102 general mathematics, Mathematical analysis, Stein's method, Space (mathematics), Random walk, 01 natural sciences, Potential theory, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Sobolev space, 010104 statistics & probability, Distribution (mathematics), Mathematics::Probability, Convergence (routing), FOS: Mathematics, 0101 mathematics, Mathematics - Probability, Analysis, Brownian motion, Mathematics
Abstract

International audience; The original Donsker theorem says that a standard random walk converges in distribution to a Brownian motion in the space of continuous functions. It has recently been extended to enriched random walks and enriched Brownian motion. We use the Stein-Dirichlet method to precise the rate of this convergence in the topology of fractional Sobolev spaces.

Published
2019

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