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Results tagged with random-walks
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user 14302
29
votes
Accepted
A random walk with uniformly distributed steps
Here is an argument that proves the conjecture. More generally, it shows that if $X_1,\dots,X_n$ is a "generic" sequence of positive real numbers, and we form a sum by permuting the terms randomly and …
- 5,492
9
votes
Accepted
Expected Hitting Time for Simple Random Walk from origin to point (x,y) in 2D-Integer-Grid
Oops, too long for a comment:
The expectation of the time until you reach a given point other than the origin is infinite already in one dimension. To see this, let $T$ be the expected time until yo …
- 5,492
9
votes
Probability of a Random Walk crossing a straight line
Here's a gem I heard from Olle Häggström in 2003. It doesn't completely answer the question, but it's a surprisingly simple (imo) way to obtain an upper bound on $P(\alpha)$.
Suppose the walk does c …
- 5,492
19
votes
Probability of a Random Walk crossing a straight line
I believe that leonbloy's comment/hint is relevant, and whenever $\alpha$ is rational, $P(\alpha)$ is algebraic. For instance, $P(1/3)$ is simply the probability that a random walk on $\mathbb{Z}$ sta …
- 5,492
3
votes
Random path in a graph
You might be interested in Loop Erased Random Walks and David Wilson's algorithm, see for instance http://research.microsoft.com/en-us/um/people/schramm/memorial/usf-talk.ps
- 5,492