Intersecting random half spaces with a cube
[Volume de l'intersection d'un cube et de sous-espaces aleatoires]
Comptes Rendus. Mathématique, Tome 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.

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DOI : 10.1016/S1631-073X(02)02368-3
Talagrand, Michel 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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Talagrand, Michel. Intersecting random half spaces with a cube. Comptes Rendus. Mathématique, Tome 334 (2002) no. 9, pp. 807-809. doi : 10.1016/S1631-073X(02)02368-3. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02368-3/

[1] Bovier, A.; Gayrard, V. Hopfield models as generalized mean field models (Bovier, A.; Picco, P., eds.), Mathematical Aspects of Spin Glasses and Neural Networks, Progress Probab., 41, Birkhäuser, 1998, pp. 3-89

[2] Gardner, E. The space of interactions in neural networks models, J. Phys. A, Volume 21 (1988), pp. 271-284

[3] M. Shcherbina, B. Tirrozi, Rigorous solution to the Gardner problem, to appear

[4] Shcherbina, M.; Tirrozi, B. On the volume to the intersection of the sphere with random half-spaces, C. R. Acad. Sci. Paris, Série I, Volume 334 (2002), pp. 803-806

[5] Talagrand, M. 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

[7] M. Talagrand, Spin Glasses: A Challenge to Mathematicians, to appear in the Ergebnisse Series, Springer-Verlag

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