论文标题
格拉斯曼尼亚人和统一戴森·布朗尼运动的量子共同体学
Quantum cohomology of the Grassmannian and unitary Dyson Brownian motion
论文作者
论文摘要
我们研究了一类通勤马尔可夫内核，其最简单的元素描述了$ k $粒子在一个尺寸$ n $的离散圆圈上的移动，条件是不相互交流。这样的马尔可夫内核与grassmannian的量子共同体学有关，这是一个代数对象，计数分析图，从$ \ m m i \ m athbb {p}^1（\ Mathbb {c}）$到k-b-nimennian k-b-nimennian k-b-nimennian j-b-niim vector vector vector suppace of $ \ mathbb aint at coprectition的c} c} c}^n $ $ \ mathbb {p}^1（\ mathbb {c}）$。当固定k时，我们获得了约为$ n^2 $ Markov内核的任意产品的浆果定理和局部限制定理。作为这些结果的副产品，我们根据$ su（k）$上的热核得出了grassmannian的量子共同体学环的渐近公式。
We study a class of commuting Markov kernels whose simplest element describes the movement of $k$ particles on a discrete circle of size $n$ conditioned to not intersect each other. Such Markov kernels are related to the quantum cohomology ring of the Grassmannian, which is an algebraic object counting analytic maps from $\mathbb{P}^1(\mathbb{C})$ to the Grassmannian space of k-dimensional vector subspaces of $\mathbb{C}^n$ with prescribed constraints at some points of $\mathbb{P}^1(\mathbb{C})$. We obtain a Berry-Esseen theorem and a local limit theorem for an arbitrary product of approximately $n^2$ Markov kernels belonging to the above class, when k is fixed. As a byproduct of those results, we derive asymptotic formulas for the quantum cohomology ring of the Grassmannian in terms of the heat kernel on $SU (k)$.
