论文标题
$ p $ - adic随机步行及其应用于蛋白质的光谱扩散的逗留时间问题
The sojourn time problem for a $p$-adic random walk and its applications to the spectral diffusion of proteins
论文作者
论文摘要
我们考虑在紧凑型套装$ \ mathbb {z} _ {p} $的问题中，在$ p $ -Adic随机步行中的分布问题。我们依靠以前关于$ p $ addic随机步行的首次返回时间分布的研究结果，以及Takacs的结果在研究的整个随机过程中研究索期时间问题。对于$ p $ -ADIC随机步行，我们发现轨迹的平均索期时间$ \ Mathbb {z} _ {p} $，而渐近学为$ t \ rightarrow \ rightarrow \ rightarrow \ intyrot \ intyrotics在$ \ mathbb {z} _ {p} _ {p} $ sojourn Time分布的任意时刻的任意时刻。我们还讨论了我们的结果对与蛋白质构象动力学相关的放松过程的建模的一些可能应用。
We consider the problem of the distribution of the sojourn time in a compact set $\mathbb{Z}_{p}$ in the case of a $p$-adic random walk. We rely on the results of our previous studies of the distribution of the first return time for a $p$-adic random walk and the results of Takacs on the study of the sojourn time problem for a wide class of random processes. For a $p$-adic random walk we find the mean sojourn time of the trajectory in $\mathbb{Z}_{p}$ and the asymptotics as $t\rightarrow\infty$ of arbitrary moments of the distribution of the sojourn time in $\mathbb{Z}_{p}$. We also discuss some possible applications of our results to the modeling of relaxation processes related to the conformational dynamics of protein.
