标题： 当前涨落中的Dyson气体 显示英文标题

标题： Current fluctuations in the Dyson Gas

摘要： 我们研究了在Dyson气体中电流的大型波动，这是一个一维粒子系统，通过对数势相互作用并受到随机噪声的影响。 我们将宏观波动理论应用于Dyson气体，并推导出两个耦合的偏微分方程，描述密度和动量的演化。 这些方程是非线性和非局部的，边界条件是混合的：一些在初始时间，另一些在最终时间。 如果初始条件可以波动（退火设置），这个边值问题是可以处理的。 我们计算了生成所有电流累积量的累积量生成函数。 显示英文摘要

摘要： We study large fluctuations of the current in a Dyson gas, a 1D system of particles interacting through a logarithmic potential and subjected to random noise. We adapt the macroscopic fluctuation theory to the Dyson gas and derive two coupled partial differential equations describing the evolution of the density and momentum. These equations are nonlinear and non-local, and the `boundary' conditions are mixed: some at the initial time and others at the final time. If the initial condition can fluctuate (annealed setting), this boundary-value problem is tractable. We compute the cumulant generating function encoding all the cumulants of the current.