论文标题
与Gibbs点过程相关的随机Schrödinger操作员的综合密度的渐近行为
Asymptotic behaviors of the integrated density of states for random Schrödinger operators associated with Gibbs Point Processes
论文作者
论文摘要
研究了与Gibbs点过程相关的非阳性电位的Schrödinger算子的综合密度的渐近行为。结果表明，对于某些Gibbs点过程，$ n（λ）$的领先术语为$λ\ downarrow- \ infty $与Poisson Point Process相吻合，这是已知的。此外，对于某些与成对相互作用相对应的Gibbs点过程，确定$ n（λ）$的领先术语确定为$λ\ downarrow- \ infty $，这与Poisson Point Possce的指数不同。
The asymptotic behaviors of the integrated density of states $N(λ)$ of Schrödinger operators with nonpositive potentials associated with Gibbs point processes are studied. It is shown that for some Gibbs point processes, the leading terms of $N(λ)$ as $λ\downarrow-\infty$ coincide with that for a Poisson point process, which is known. Moreover, for some Gibbs point processes corresponding to pairwise interactions, the leading terms of $N(λ)$ as $λ\downarrow-\infty$ are determined, which are different from that for a Poisson point process.
