论文标题
平面低温库仑气体：分离和等分分配
The planar low temperature Coulomb gas: separation and equidistribution
论文作者
论文摘要
我们认为平面库仑系统由大量$ n $排斥点的电荷组成，在低温方向上，倒数温度$β$至少在$ n $中以$ n \ longrightArrow \ indrightArrow \ infty \ infty $，即$β\ gtrsim \ gtrsim \ log n $。在外部电势的适当条件下，我们证明了与相应平衡度量（在给定外场）相对于相应平衡度量的高概率均匀分离和等分分配的影响。我们的结果概括了有关fekete配置的早期结果，即情况$β= \ infty $。还有一些辅助结果可能具有独立的关注。例如，我们的等均分配证明方法（“ Landau的方法”的一种变体）适用于统一分离并满足某些采样和插值不平等的一般配置家庭。
We consider planar Coulomb systems consisting of a large number $n$ of repelling point charges in the low temperature regime, where the inverse temperature $β$ grows at least logarithmically in $n$ as $n \longrightarrow \infty$, i.e., $β\gtrsim \log n$. Under suitable conditions on an external potential we prove results to the effect that the gas is with high probability uniformly separated and equidistributed with respect to the corresponding equilibrium measure (in the given external field). Our results generalize earlier results about Fekete configurations, i.e., the case $β=\infty$. There are also several auxiliary results which could be of independent interest. For example, our method of proof of equidistribution (a variant of "Landau's method") works for general families of configurations which are uniformly separated and which satisfy certain sampling and interpolation inequalities.
