单边碰撞布朗运动的标度极限
Scaling limit for Brownian motions with one-sided collisions
摘要：
我们考虑具有单侧碰撞的布朗运动，这意味着每个粒子都在其右邻居处反射。对于有限数量的粒子，一个Schütz型公式推导出的过渡概率。我们研究了一个具有周期性初始组态的无限大系统，即粒子在零时刻位于整数格点。粒子的有限子集的位置的联合分布被表示为一个Fredholm行列式与核定义一个有符号的行列式点过程。在适当的大时间尺度限制下，粒子位置的波动由Airy $_1$过程描述。
英文摘要：
We consider Brownian motions with one-sided collisions, meaning that each particle is reflected at its right neighbour. For a finite number of particles a Schütz-type formula is derived for the transition probability. We investigate an infinite system with periodic initial configuration, that is, particles are located at the integer lattice at time zero. The joint distribution of the positions of a finite subset of particles is expressed as a Fredholm determinant with a kernel defining a signed determinantal point process. In the appropriate large time scaling limit, the fluctuations in the particle positions are described by the Airy$_1$ process.
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