منابع مشابه
Parisi Phase in a Neuron
Pattern storage by a single neuron is revisited. Generalizing Parisi's framework for spin glasses we obtain a variational free energy functional for the neuron. The solution is demonstrated at high temperature and large relative number of examples , where several phases are identified by thermodynam-ical stability analysis, two of them exhibiting spontaneous full replica symmetry breaking. We g...
متن کاملThe Untruncated Marinari-parisi Superstring
It is shown that the bosonic angular degrees of freedom in the one dimensional Marinari-Parisi superstring can be integrated out exactly in the Hamiltonian formulation without having to perform the Dabholkar truncation. The resulting Hamiltonian is that of a supersymmetric Calogero system plus a four fermions interaction. This extra interaction vanishes for all physical states with fermion numb...
متن کاملA Question about Parisi Functional
We conjecture that the Parisi functional in the Sherrington-Kirkpatrick model is convex in the functional order parameter. We prove a partial result that shows the convexity along “one-sided” directions. An interesting consequence of this result is the log-convexity of Lm norm for a class of random variables.
متن کاملNumerical Solution of Altarelli-Parisi Equations
We discuss numerical solution of Altarelli-Parisi equations in a Laguerre-polynomial method and in a brute-force method. In the Laguerre method, we get good accuracy by taking about twenty Laguerre polynomials in the flavor-nonsinglet case. Excellent evolution results are obtained in the singlet case by taking only ten Laguerre polynomials. The accuracy becomes slightly worse in the small and l...
متن کاملOn Differentiability of the Parisi Formula
It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application of differentiability to prove non self-averaging of the overlap outside of the...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2006
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2005.03.001