Timeline for Existence of Limiting Distribution for Moving Regions in Stat. Phys. Models
Current License: CC BY-SA 3.0
6 events
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| Aug 18, 2015 at 16:02 | history | edited | Carlo Beenakker | CC BY-SA 3.0 |
ImageShack to imgur
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| May 4, 2010 at 22:03 | comment | added | passing by | I haven't been able to think of anything that is similar where there isn't convergence. I have a few silly examples of pieces of infinite Markov chains where there isn't convergence, but they are very made-up and lack convergence for some straightforward projections. Essentially, these sorts of chains sometimes don't converge if labellings close to 0 are both persistent and have long-term and long-range influence; neither of those are true here. As for the limiting distribution, I expect it to be worse than the Derridas' process, which is already hard to find (though solved now). | |
| May 4, 2010 at 21:24 | history | edited | Alekk | CC BY-SA 2.5 |
simulations rechecked
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| May 4, 2010 at 20:53 | comment | added | Alekk | Do you have any example of a similarly defined process where there is no convergence ? Is it reasonable to expect a nice description of the limiting distribution (Boltzman distribution of a concrete energy function for example?) | |
| May 4, 2010 at 19:31 | comment | added | passing by | Hi Alekk, thanks for the reply. I've never known how to interpret 'geometric' pictures to conclude anything about limiting distributions - any comments on this? I have run a number of simulations looking at the long-time distribution of various linear functionals to see if they have limits, since the computer can draw a bunch of empirical CDFs on top of each other, and the answer seems to be yes for the random functionals my computer has turned up... | |
| May 4, 2010 at 19:08 | history | answered | Alekk | CC BY-SA 2.5 |