Questions tagged [random-walk]

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

619 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 ...
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335 views