Stretched exponential decay for subcritical parking times on
Stretched exponential decay for subcritical parking times on
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亚临界停车时间的拉伸指数衰减
DOI：
10.1002/rsa.21001
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发表时间：
2021
影响因子：
1
通讯作者：
Sivakoff, David
中科院分区：
文献类型：
--
作者：
Damron, Michael;Lyu, Hanbaek;Sivakoff, David
在 的每个顶点，放置一辆车，其概率为 1 −p 的空闲停车位。汽车进行独立随机行走并停在空位上，使其可以通行。存在一个转变 atp= 1/2：原点是 a.s. 当 p< 1/2 时，有有限多辆不同的汽车访问过；当 p≥ 1/2 时，有无数辆不同的汽车访问过。此外，a.s. 如果p≤ 1/2，所有汽车都停车，有些汽车在p> 1/2时从不停车。对于smallp，我们证明汽车最初在原点的停车时间满足 。 Ford= 1，这些不等式适用于 p< 1/2。相反，当p> 1/2且d= 1时，Bramson-Lebowitz方法意味着原点停车时间的尾部衰减为 。我们的指数 d/(d+ 2) 也与之前在移动障碍物的情况下获得的指数不同。
At each vertex of , place a car with probabilitypor vacant parking spot with probability 1 −p. Cars perform independent random walks and park at vacant spots, rendering them passable. There is a transition atp= 1/2: the origin is a.s. visited by finitely many distinct cars whenp< 1/2, and by infinitely many whenp≥ 1/2. Furthermore, a.s. all cars park ifp≤ 1/2 and some never park forp> 1/2. For smallp, we prove that the parking time of the car initially at the origin satisfies . Ford= 1, these inequalities hold forp< 1/2. In contrast, whenp> 1/2 andd= 1, methods of Bramson–Lebowitz imply that the tail of the parking time of the spot of the origin decays like . Our exponentd/(d+ 2) also differs from those previously obtained in the case of moving obstacles.