论文标题
高阶波动场和正交双重性多项式
Higher order fluctuation fields and orthogonal duality polynomials
论文作者
论文摘要
受[1]和[8]的作品的启发，我们介绍了我们所谓的$ k $ ther阶波动场并研究其缩放限制。这种结构是在粒子系统的背景下，具有正交自偶性的特性。这种二元性为我们提供了一种设置，在该设置中，我们能够将这些字段解释为众所周知的密度波动场的某种离散类似物。我们表明，$ k $ -th订单字段的弱极限满足了一个递归的martingale问题，该问题正式与与广义的Ornstein-Uhlenbeck过程的$ k $ th-power相关的SPDE。
Inspired by the works in [1] and [8] we introduce what we call $k$-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This type of duality provides us with a setting in which we are able to interpret these fields as some type of discrete analogue of powers of the well-known density fluctuation field. We show that the weak limit of the $k$-th order field satisfies a recursive martingale problem that formally corresponds to the SPDE associated with the $k$th-power of a generalized Ornstein-Uhlenbeck process.
