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{\Large המחלקה למתמטיקה, בן-גוריון}

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{\Huge הסתברות ותורה ארגודית}\\[0.2\baselineskip]

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\textbf{ב}\emph{יום שלישי, 14 באפריל, 2015}
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\textbf{בשעה} \emph{10:50 -- 12:00}
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\textbf{ב}\emph{Math -101}

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ההרצאה

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{\Large\bfseries The complexity of spherical p-spin models - a second moment approach\par}
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תינתן על-ידי
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{\large\scshape Eliran Subag 
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  (Weizmann Institute)
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\textbf{תקציר:}
  The Hamiltonian of the spherical p-spin spin glass model is a smooth Gaussian field on the N-dimensional sphere. Let \$Crt\_N(u)\$ denote the number of its critical points below \$Nu\$. In a recent study Auffinger, Ben Arous, and Cerny computed the mean of \$Crt\_N(u)\$ and its exponential growth rate, as N goes to infinity. Our work focuses on the computation of the second moment. We prove that the ratio of second to first moment squared goes to 1, as N goes to infinity. An immediate consequence of this is that \$Crt\_N(u)\$ concentrates around its mean: \$Crt\_N(u)\$ normalized by its mean goes to 1 in L\^{}2 and thus in probability. Joint work with Ofer Zeitouni.
  


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