AI 中文总结
研究谢林顿 - 柯克帕特里克模型在零外场及β>1时帕里西测度的支撑情况，通过反证法，利用高斯科尔 - 霍普夫表示导出微分不等式，证明此时帕里西测度具有无限支撑。
AI 中文摘要
我们证明，在零外场且每个逆温度β>1时，谢林顿 - 柯克帕特里克模型的帕里西测度具有无限支撑。证明采用反证法，假设帕里西测度是有限支撑的，利用帕里西偏微分方程解的高斯科尔 - 霍普夫表示导出一个微分不等式，该不等式与贾甘纳特和托巴斯科（2017）建立的帕里西极小值的变分最优条件不兼容。
英文摘要
We prove that, at zero external field and for every inverse temperature $β>1$, the Parisi measure of the Sherrington-Kirkpatrick model is supported on an interval $[0,q_β]$, with a smooth density on $(0,q_β)$ and an atom at $q_β$. The primary difficulty is to exclude gaps in the support. On such a gap, the optimality conditions for the Parisi measure would force the second derivative of the associated self-consistency function $Γ$ to cross zero downward. We establish that it can only cross upward by showing that at a zero of $Γ''$, the derivative $Γ'''$ is a positive linear combination of two nonnegative covariances, one of which is strictly positive.
Comments24 pages; simplified proofs and improved exposition
