论文标题
平均场自旋眼镜中的非凸相互作用
Nonconvex interactions in mean-field spin glasses
论文作者
论文摘要
我们提出了一个具有两分结构的平均场自旋玻璃极限的猜想，并表明猜想的极限是上限。猜想的极限是用无限维汉密尔顿 - 雅各比方程的解决方案来描述的。该问题的基本困难是该方程式中的非线性不是凸。我们还质疑以鞍点问题来表征这种猜想极限的可能性。
We propose a conjecture for the limit of mean-field spin glasses with a bipartite structure, and show that the conjectured limit is an upper bound. The conjectured limit is described in terms of the solution of an infinite-dimensional Hamilton-Jacobi equation. A fundamental difficulty of the problem is that the nonlinearity in this equation is not convex. We also question the possibility to characterize this conjectured limit in terms of a saddle-point problem.
