论文标题
吉布斯歧管
Gibbs Manifolds
论文作者
论文摘要
Gibbs歧管是指数图下对称矩阵的仿射空间的图像。它们出现在诸如优化，统计和量子物理学等应用中，它们扩展了感谢您的几何作用。 Gibbs品种是在Gibbs歧管上消失的所有多项式的零基因座。我们计算这些多项式，并表明吉布斯品种是低维的。我们的理论应用于各种场景，包括基质铅笔和量子最佳传输。
Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum~physics, where they extend the ubiquitous role of toric geometry. The Gibbs variety is the zero locus of all polynomials that vanish on the Gibbs manifold. We compute these polynomials and show that the Gibbs variety is low-dimensional. Our theory is applied to a wide range of scenarios, including matrix pencils and quantum optimal transport.
