A Variational Characterization of the Speed of a One-Dimensional Self- Repellent Random Walk
A Variational Characterization of the Speed of a One-Dimensional Self- Repellent Random Walk
复制标题
一维自排斥随机游走速度的变分表征
DOI：
10.1214/aoap/1177005273
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发表时间：
1993
影响因子：
1.8
通讯作者：
F. Hollander
中科院分区：
文献类型：
--
作者：
A. Greven;F. Hollander
我们用NI x NI矩阵的单参数族的最大特征值给出了0* (a)的一个表征。这允许我们证明0* (a)是自排斥强度a的解析函数。除了速度外，我们还证明了随机漫步局部时间的一个极限律。所使用的技术使我们能够处理涉及多个交叉点的更一般形式的自我排斥。我们给出了一个等价于a -* 0*(a)（严格地）递增的偏微分不等式。对这种不平等的验证仍有待证实。
We give a characterization of 0* (a) in terms of the largest eigenvalue of a one-parameter family of NI x NI matrices. This allows us to prove that 0* (a) is an analytic function of the strength a of the self-repellence. In addition to the speed we prove a limit law for the local times of the random walk. The techniques used enable us to treat more general forms of self-repellence involving multiple intersections. We formulate a partial differential inequality that is equivalent to a -* 0*(a) being (strictly) increasing. The verification of this inequality remains open.