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Start at the point . At each time step, choose a point uniformly at random from , and then move half way from the current position to the chosen point.
In other words, at each time step transition from to one of .
After time steps measure the distance from the starting position.
What is the distribution of distances as ? What is the expected distance?
I understand how to find stationary distributions for finite Markov chains, but this is a bit beyond me. What topics would be needed to answer this, or is there a general approach to answer questions of this form? 98.190.129.147 ( talk) 23:41, 23 May 2019 (UTC)
Mathematics desk | ||
---|---|---|
< May 22 | << Apr | May | Jun >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Start at the point . At each time step, choose a point uniformly at random from , and then move half way from the current position to the chosen point.
In other words, at each time step transition from to one of .
After time steps measure the distance from the starting position.
What is the distribution of distances as ? What is the expected distance?
I understand how to find stationary distributions for finite Markov chains, but this is a bit beyond me. What topics would be needed to answer this, or is there a general approach to answer questions of this form? 98.190.129.147 ( talk) 23:41, 23 May 2019 (UTC)