We find an asymptotic expression of the volume of the intersection of the N dimensional sphere with p = alphaN random half spaces when a is less than a critical value. This expression coincides with the one found by Gardner [3] using replica calculations. We get also the same value for alpha(c). Our proof is rigorous and based on the cavity method. The required decay of correlations is obtained by means of a geometrical argument which holds for general Hamiltonians. To cite this article: M. Shcherbina, B. Tirozzi, C R. Acad. Sci. Paris, Ser. I 334 (2002) 803-806. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
On the volume of the intersection of a sphere with random half spaces / Maria, Shcherbina; Tirozzi, Benedetto. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 334:9(2002), pp. 803-806. [10.1016/s1631-073x(02)02345-2]
On the volume of the intersection of a sphere with random half spaces
TIROZZI, Benedetto
2002
Abstract
We find an asymptotic expression of the volume of the intersection of the N dimensional sphere with p = alphaN random half spaces when a is less than a critical value. This expression coincides with the one found by Gardner [3] using replica calculations. We get also the same value for alpha(c). Our proof is rigorous and based on the cavity method. The required decay of correlations is obtained by means of a geometrical argument which holds for general Hamiltonians. To cite this article: M. Shcherbina, B. Tirozzi, C R. Acad. Sci. Paris, Ser. I 334 (2002) 803-806. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
