# Questions tagged [random-walks]

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### Random process on a sequence of rolls of an $n$-sided die

Let $\ X:=X_{k\,n}\$ be a random variable of a $n$-sided die where $\Pr(X=i)=\frac{1}{n}$ for each $i\in\{1,2,\ldots,n\},\$ where $\ k\in\{1, 2, \ldots,n\}\$ and $\ n\$ are fixed. Let $t$ be a ...
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### Arcsine law for gaussian random walk

Consider the random walk $S_i=Z_1+\dots+Z_i$, where the $Z_i$'s are iid $N(0,1)$ and $i\in\{1\dots n\}$. Is there an arcsine law, similar to the one for the $\{\pm 1\}$ case?
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### Winning money from random walks?

The same question was posted on StackExchange. Informal problem description Assume that we have a stock whose price behaves exactly like a Wiener process. (There are multiple reasons why this is not ...
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### Smooth functions that resemble random walks

If the Riemann hypothesis holds, then the Mertens function $M(n)\equiv\sum_{x\leq n} \mu(n)$ behaves much like a 1D random walk. This includes the statements that $M(n)$ changes sign infinitely often ...
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### Gaussian bounds for discrete (graph) Dirichlet heat kernel

(this is an attempt to refine a previous question; I was told that it would be better to create a new question than edit the previous one, I hope this is the correct ettiquete.) Let $\Omega$ be a ...
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### Ihara zeta function and closed paths and trails

Let $\Gamma$ be a finite graph. There seem to be two definitions of closed path in the literature. In one, a closed path is just a walk whose starting vertex is the same as the ending vertex. (Let us ...
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