# Questions tagged [random-walk]

For questions on random walks, a mathematical formalization of a path that consists of a succession of random steps.

609 questions
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### Brownian Motion in Confined space, any results?

I am searching for work regarding Brownian motion in a confined space, like a sphere or a cylinder, where the wall will serve as reflection boundary. I am wondering if it is possible to derive results ...
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### Random matrices, eigenvalue distribution.

I just investigated randn(1024) + 1i*randn(1024), a 1024x1024 complex valued matrix with elements both real part and imaginary part drawn from $\mathcal{N}(\mu = 0, \sigma = 1)$. I was a bit surprised ...
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### Probability random walk remains bounded

Consider a simple unbiased random walk on the discrete line starting at $0$. Fix a number $n$. As a function of $k$, what is the probability that the walk remains bounded in $\{-n,\ldots,n\}$ for the ...
The following question is somewhat related to: Asymmetric random walk Let $(X_i)_{i=1}^n$ be a sequence of i.i.d. random variables with $\Pr(X_i=1)=\Pr(X_i=-1)=1/2$. Let $S_0=0$ and, for $1\le i\le ... 0answers 750 views ### Why are random walks in dimensions 3 or higher transient? I watched this PBS video a while ago (relevant part here) and have been trying to get my head around the idea of transient walks. The video says that a recurrent random walk is one that is guaranteed ... 0answers 94 views ### How can I generate a random walk on the unitary group$U(n)$? I'm interested in generating a random walk on U(n) using a computer: any references on this topic or related / requisite topics would be helpful. Specific suggestions that discuss the problem ... 0answers 105 views ### A Proof that the distribution becomes unitary after N step 2D lattice random Walk I am working with random walks and http://mathworld.wolfram.com/RandomWalk2-Dimensional.html says that "Amazingly, it has been proven that on a two-dimensional lattice, a random walk has unity ... 0answers 74 views ### Predator-Prey Pursuit-Evasion via Random Walks on a Graph Let$G = (V, E)$be a connected, undirected graph. We begin by placing$a$predators and$b$prey on the graph: each one is placed at a node chosen uniformly at random. Each predator and each prey ... 0answers 143 views ### Random walk with centered increments Let$X_1, X_2,\cdots$be a sequence of independent, identically distributed random variables and$\displaystyle S_n=\sum_{i=1}^{n}X_i$. Then$EX_{1} <0$if, and only if ,$\displaystyle\lim_{n \...
Consider a random walk $(X_n)$ on the graph below, where we jump from a given vertex to one of its adjacent vertices with equal probability. I want to find: the probability that we hit $A$ before ...