M ay 2 00 4 A central limit theorem for weighted averages of spins in the high temperature region of the Sherrington - Kirkpatrick model
نویسنده
چکیده
In this paper we prove that in the high temperature region of the SherringtonKirkpatrick model for a typical realization of the disorder the weighted average of spins ∑ i≤N tiσi will be approximately Gaussian provided that maxi≤N |ti|/ ∑ i≤N t 2 i is small.
منابع مشابه
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In his recent paper [6] Michel Talagrand gave a rigorous proof of the Parisi formula for the free energy of the Sherrington-Kirkpatrick model. In the present paper we utilize the methodology developed in [6] to compute the thermodynamic limit of the free energy of the set of configurations with the fixed average of spins N−1 ∑ i≤N σi = uN as uN → u ∈ [−1, 1].
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