On the volume of the intersection of a sphere with random half spaces

DOI10.1016/S1631-073X(02)02345-2zbMath1002.60005MaRDI QIDQ1600172

Brunello Tirozzi, Mariya Shcherbina

Publication date: 1 January 2003

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

zbMATH Keywords

Gaussian random variablevolume of intersection\(N\)-dimensional sphere

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Limit theorems in probability theory (60F99)

Related Items (2)

Approximate Voronoi cells for lattices, revisited ⋮ Intersecting random half spaces with a cube

Cites Work

• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• The Sherrington-Kirkpatrick model: A challenge for mathematicians
• Intersecting random half-spaces: Toward the Gardner-Derrida formula.
• Replica symmetry breaking and exponential inequalities for the Sherrington-Kirkpatrick model.
• The replica-symmetric solution without replica trick for the Hopfield model
• General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity
• Self averaging and the space of interactions in neural networks
• On the replica symmetric equations for the Hopfield model
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