论文标题
在一维湿润的边缘
At the edge of a one-dimensional jellium
论文作者
论文摘要
我们认为一维经典的wigner jellium，不一定是电荷中性，允许电子在背景电荷的支持之外存在。该模型可以看作是一维的库仑气体，其中外场是由间隔的涂抹背景产生的。这是真正的一维库仑气体，而不是一维日志气体。当且仅当总背景电荷大于电子数量数量时，系统就存在。对于各种背景，我们在背景支持的边缘显示了与点过程的收敛。特别是，这提供了对正确粒子波动的渐近分析。我们的分析表明，这些波动不是普遍的，从某种意义上说，根据背景，尾巴范围从指数到高斯样行为，包括例如Tracy-Widom样行为。我们还获得了粒子系统的顺序统计量的Renyi-type概率表示，超出了背景的支持。
We consider a one-dimensional classical Wigner jellium, not necessarily charge neutral, for which the electrons are allowed to exist beyond the support of the background charge. The model can be seen as a one-dimensional Coulomb gas in which the external field is generated by a smeared background on an interval. It is a true one-dimensional Coulomb gas and not a one-dimensional log-gas. The system exists if and only if the total background charge is greater than the number of electrons minus one. For various backgrounds, we show convergence to point processes, at the edge of the support of the background. In particular, this provides asymptotic analysis of the fluctuations of the right-most particle. Our analysis reveals that these fluctuations are not universal, in the sense that depending on the background, the tails range anywhere from exponential to Gaussian-like behavior, including for instance Tracy-Widom-like behavior. We also obtain a Renyi-type probabilistic representation for the order statistics of the particle system beyond the support of the background.
