Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Difference in random walk description

  1. Jun 7, 2015 #1
    We studied random walk starting from a probability conservation : p(x,t)=p(x+dx,t+dt)+p(x-dx,t+dt)

    Which means the particle can go left or right by dx in time dt.

    The solution of the differential equation starting from a delta is a gaussian, which means the particle could go apparently at different speed than dx in dt.

    Where does this difference comes from ?
     
  2. jcsd
  3. Jun 7, 2015 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Gaussian results from the fact that you adding the results of an "infinite" number of "infinitesimal" steps, which are independent and where each step can be + or -. Essentially it is the result of the central limit theorem applied to the limit of a binomial distribution.
     
  4. Jun 8, 2015 #3
    So after a time dt it could be that we added an infinite number of + hence reaching infinity ?

    What could we do if we want a maximal speed ? So that it becomes compatible with relativity.
     
  5. Jun 8, 2015 #4

    mathman

    User Avatar
    Science Advisor
    Gold Member

    Each step (+ or -dx) takes time dt. The central limit theorem describes the result of integrating over time. The distance traveled in time T has a Gaussian distribution with variance proportional to T.

    I don't understand what you are trying to with infinity. If all the steps are in the same direction, it is not a random walk.
     
  6. Jun 9, 2015 #5
    Adding only plus is a limit case, when the time is small paths going around the origin are prefered but then this difference gets smaller. but what i mean is that the speed at time dt can reach infinity. And i look for a method to avoid this.
     
  7. Jun 9, 2015 #6

    mathman

    User Avatar
    Science Advisor
    Gold Member

    What do you mean by "small paths going around the origin"? I thought you were describing a 1 dimensional case.
     
  8. Jun 10, 2015 #7
    It is rather through or at the origin.
     
  9. Jun 10, 2015 #8

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The basic point is that each tiny step can be + or -. To get infinite speed you need a preponderance of one or the other.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Difference in random walk description
  1. Random Walk (Replies: 2)

  2. Random walk (Replies: 2)

Loading...