竞争粒子系统前沿不变测度的刻画
Characterization of invariant measures at the leading edge for competing particle systems
摘要：
我们研究系统的粒子在一条线上有一个最大的，是局部有限的，并与独立的增量发展。"准定态“定义为在由能隙变量生成的σ-代数上的概率测度，对于这些测度，粒子间能隙的联合分布在时间演化下是不变的。例子是密度为ρ（dx）=e^{-sx}s dx的泊松过程，其中s>0，以及这些测度的线性叠加。相反，我们证明了，任何独立动力学的准定态，具有指数有界的粒子积分密度，对应于密度ρ（dx）=e^{-sx}s dx的泊松过程的叠加，其中s>0，限制到相关的σ-代数。与这个问题有一定关联的系统包括统计力学的自旋玻璃模型，其中点过程代表不同"纯态“自由能的集合，时间演化对应于增加一个自旋变量，上述泊松测度对应于所谓的REM态。
英文摘要：
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the σ-algebra generated by the gap variables, for which joint distribution of gaps between particles is invariant under the time evolution. Examples are provided by Poisson processes with densities of the form ρ(dx)=e^{-sx}s dx, with s>0, and linear superpositions of such measures. We show that, conversely, any quasi-stationary state for the independent dynamics, with an exponentially bounded integrated density of particles, corresponds to a superposition of Poisson processes with densities ρ(dx)=e^{-sx}s dx with s>0, restricted to the relevant σ-algebra. Among the systems for which this question is of some relevance are spin-glass models of statistical mechanics, where the point process represents the collection of the free energies of distinct ``pure states,'' the time evolution corresponds to the addition of a spin variable and the Poisson measures described above correspond to the so-called REM states.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
