# Tagged Questions

72 views

### N random walkers that hit node v in a graph

Consider a finite, undirected graph G, with uniform edge weights. Assume that there are n number of random walkers that will start at different nodes (lets say n=3, hence the random walkers will start ...
185 views

### First Collision Time for k Random Walkers on a Torus

I consider $k$ random walkers on $\mathbb{Z}^{d}/n \mathbb{Z}^{d}$, the $d$-dimensional torus of side length $n$. More precisely, I will define a Markov chain $Z_{t} = (X_{t}[1], \ldots, X_{t}[k])$ ...
497 views

### Hitting time probability in a Random Walk with possibility to die.

A Random Walker can move of one unit to the right with probability $p$, to the left with probability $q$ and it can jump again to the starting point with probability $r$ and die. Naturally $p+q+r=1$. ...
211 views

### Stationary distribution for directed graph

I want to implement the algorithm of graph partitioning of sparse directed graph. In this algorithm after computing the transition matrix ,we should compute the stationary distribution of the random ...
203 views

### Approximating a hitting time for some state using the stationary distribution?

Provided a random walk on a bounded interval, with step probabilities, $p$ and $q$ and a stationary distribution $\pi$, how "bad" of an approximation is to assume that the hitting time for a position ...
1k views

### Expected Hitting Time for Simple Random Walk from origin to point (x,y) in 2D-Integer-Grid

Consider a simple random walk on the lattice $\mathbb Z^2$ starting at the origin $(0,0)$ where in each step, one of the four adjacent vertices in chosen uniformly at random, i.e. with probability ...
207 views

### Extending Wald's equation to two classes of i.d. random variables?

I try to adopt Wald's equation to a slightly more complex problem. In fact, after a full day, I found some solution now, but it has a confusing argument in the middle. Perhaps somebody can help me at ...
575 views

### Markov chains: invariant measures and explosion

The following seems like such an elementary question, but I didn't get anywhere with it. Suppose you are considering a Markov chain in continuous time which is transient and has an invariant measure ...
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### Distributions induced by (weighted) random walks on the integer lattice

Consider an integer lattice $\mathbb{Z}^2$ where grid points are separated by a distance $h$. Loosely speaking, a random walk of length $k$ is a sequence of lattice points $(x_1,\cdots,x_k)$ ...
356 views

### MCMC with progressive demollification of delta distributions

Edit: I simplified the example to a canonical case for clarity. Given an integral $\int_{\Omega}{g(\mathbf{x})}$ with a well-posed integrand $g(\mathbf{x})$ defined on some multidimensional space ...
546 views

### probability distribution of hitting nodes on a finite graph random walk

Consider a finite, undirected, scale-free graph $\{G}$, with uniform edge weights. We define a truncated random walk on $\{G}$ as a random walk that continues for exactly $\{k}$ steps. For an ...
Let $p$ be a parameter in $]0,1[$. Let $(X_k)_{k\geq 0}$ be an independent, identically distributed sequence of random variables, such that each $X_k$ takes values only in \$\lbrace -1, \frac{1-p}{p} ...