Title: Local time of Levy random walks: a path integral approach Show Chinese title

Title: Levy随机游走的局部时间：路径积分方法

Abstract: Local time of a stochastic process quantifies the amount of time that sample trajectories $x(\tau)$ spend in the vicinity of an arbitrary point $x$. For a generic Hamiltonian, we employ the phase-space path-integral representation of random walk transition probabilities in order to quantify the properties of the local time. For time-independent systems, the resolvent of the Hamiltonian operator proves to be a central tool for this purpose. In particular, we focus on local times of Levy random walks (or Levy flights), which correspond to fractional diffusion equations. Show Chinese abstract

Abstract: 随机过程的局部时间量化了样本轨迹$x(\tau)$在任意点$x$附近的停留时间。 对于一般的哈密顿量，我们采用随机行走转移概率的相空间路径积分表示法来量化局部时间的性质。 对于时间不变的系统，哈密顿算符的预解式被证明是这一目的的核心工具。 特别是，我们关注 Levy 随机游走（或 Levy 飞行）的局部时间，它们对应于分数阶扩散方程。