Comptes Rendus
no. 9
Intersecting random half spaces with a cube
[Volume de l'intersection d'un cube et de sous-espaces aleatoires]
Michel Talagrand1
1 Équipe d'analyse, boı̂te 186, ESA associée au CNRS, Université Paris VI, 4, place Jussieu, 75230 Paris cedex 05, France
Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 807-809.

Nous calculons la cardinalité typique de l'intersection du cube discret {−1,1}N et de M demi-espaces aleatoires, quand M est une petite proportion de N.

We compute the typical number of points of the discrete cube {−1,1}N that belong to the intersection of M random half-spaces, when M is a small proportion of N.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02368-3

Michel Talagrand 1

1 Équipe d'analyse, boı̂te 186, ESA associée au CNRS, Université Paris VI, 4, place Jussieu, 75230 Paris cedex 05, France 
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Michel Talagrand. Intersecting random half spaces with a cube. Comptes Rendus. Mathématique, Volume 334 (2002) no. 9, pp. 807-809. doi : 10.1016/S1631-073X(02)02368-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02368-3/

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[5] M. Talagrand Intersecting random half spaces: towards the Gardner–Derrida formula, Ann. Probab., Volume 28 (2000), pp. 725-758

[6] M. Talagrand, On the Gaussian perceptron at high temperature, Anal. Geom. Math. Phys., to appear

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