The extremal process of critical points of the pure p-spin spherical spin glass model
The extremal process of critical points of the pure p-spin spherical spin glass model
复制标题
纯p-自旋球形自旋玻璃模型临界点的极值过程
DOI：
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
O. Zeitouni
中科院分区：
文献类型：
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作者：
Eliran Subag;O. Zeitouni
最近，利用矩量计算得到了关于p-自旋球自旋玻璃模型哈密顿量临界点的精确结果。特别地，这些矩计算允许评估基态的前导项，即，全球最低。本文研究了临界点的极值点过程，即在基态附近所有临界值所对应的点过程。我们证明了后者在分布上收敛于指数强度的泊松点过程。特别是，我们确定了正确的中心的基态，并证明了收敛分布的中心最小值（减）Gumbel变量。这些结果是相同的，得到一个序列的i.i.d变量，正确规范化，即，我们表明，该模型是在REM的普适性类。
Recently, sharp results concerning the critical points of the Hamiltonian of the p-spin spherical spin glass model have been obtained by means of moments computations. In particular, these moments computations allow for the evaluation of the leading term of the ground-state, i.e., of the global minimum. In this paper, we study the extremal point process of critical points—that is, the point process associated to all critical values in the vicinity of the ground-state. We show that the latter converges in distribution to a Poisson point process of exponential intensity. In particular, we identify the correct centering of the ground-state and prove the convergence in distribution of the centered minimum to a (minus) Gumbel variable. These results are identical to what one obtains for a sequence of i.i.d variables, correctly normalized; namely, we show that the model is in the universality class of REM.
关于超临界高斯自由场极值过程的注记
影响因子：
0.5
作者：
A. Chiarini; A. Cipriani;R. S. Hazra
通讯作者：
R. S. Hazra
影响因子：
2
作者：
L. Arguin;Anton Bovier;N. Kistler
通讯作者：
L. Arguin;Anton Bovier;N. Kistler