On the Gaussian Perceptron at High Temperature |
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| Authors: | Michel Talagrand |
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| Institution: | (1) Equipe d'Analyse-Tour 46, ESA au CNRS No. 7064, Université Paris VI, 4 Pl. Jussieu, 75230 Paris Cedex 05, France;(2) Department of Mathematics, The Ohio State University, 231 W. 18th Ave., Columbus, OH, 43210-1174, U.S.A |
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| Abstract: | For  =(
i
)
i N
 
N
={–1,1}
N
, define where (g
k
i
)
iN,kM
are i.i.d. N(0,1), and where u is bounded and Borel measurable. When M is a small proportion  of N, we study the system with random Hamiltonian H, at temperature 1. When is small enough, we prove that the overlap of two configurations taken independently at random for Gibbs' measure is nearly constant, with a correct estimate of the size of its fluctuations. |
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| Keywords: | replica-symmetry pure state perceptron |
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