Simulating a Random Walk with Constant Error

用一副纸牌模拟简单随机游走

Simulating Simple Random Walks With a Deck of Cards

本文研究用有限且均匀花色的纸牌模拟格点对称简单随机游走时的偏差，刻画 $N=cn$ 下全变差距离的 Gaussian 极限，并给出满足误差阈值所需牌数及超几何分布向多项分布的收敛。

生成函数与Abdelkader的随机游走模型

Generating functions and Abdelkader's random walk model

本文将Abdelkader提出的一类随机游走问题与Moran游走模型建立联系，揭示了两者之间的关联。

Conservative and semiconservative random walks: recurrence and transience

In the present paper we define conservative and semiconservative random walks in $\mathbb{Z}^d$ and study different families of random walks. The family of symmetric random walks is one of the families of conservative random walks, and simple (Pólya) random walks are their representatives. The classification of random walks given in the present paper enables us to provide a new approach to random walks in $\mathbb{Z}^d$ by reduction to birth-and-death processes. We construct nontrivial examples of recurrent random walks in $\mathbb{Z}^d$ for any $d\geq3$ and transient random walks in $\mathbb{…

Random Walk in an Alcove of an Affine Weyl Group, and Non-Colliding Random Walks on an Interval

We use a reflection argument, introduced by Gessel and Zeilberger, to count the number of k-step walks between two points which stay within a chamber of a Weyl group. We apply this technique to walks in the alcoves of the classical affine Weyl groups. In all cases, we get determinant formulas for the number of k-step walks. One important example is the region m>x_1>x_2>...>x_n>0, which is a rescaled alcove of the affine Weyl group C_n. If each coordinate is considered to be an independent particle, this models n non-colliding random walks on the interval (0,m). Another case models n non-collid…

Random walks with $k$-wise independent increments

We construct examples of a random walk with pairwise-independent steps which is almost-surely bounded, and for any $m$ and $k$ a random walk with $k$-wise independent steps which has no stationary distribution modulo $m$.

Random walks on generalized visible lattice points

We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspects: (1) generalized visibility along curves; (2) one random walker visible from multiple watchpoints; (3) simultaneous visibility of multiple random walkers. Moreover, we found new phenomenon in the case of multiple random walkers: for visibility along a large class of curves and for any number of random walkers, the proportion of steps at which all random walkers are visible simultaneously is almost surely larger th…