Hi, I'm trying to work out how many time a particle going on a random walk starting at the origin would pass a particular point or points for a given total number of steps. Ive simulated the problem and get approximately the same answer every time, however i'm struggling to know where to even start trying to work the number out analytically.(adsbygoogle = window.adsbygoogle || []).push({});

Problem

If two points lie on the x-axis at pointsandsand a particle starting at the origin goes on a random walk with step size-sfor a total ofbsteps, what is the average number of times it crossesNs or-s?

For the problem simulated I useds = 7 , b = 1, N = 1000

I ran the simulation 30000 times and the number I got was 37.6310, I did this by simply creating a random number between 0 and 1 if the number is > 0.5 walk left < 0.5 walk right, and incremented a counting variable every time it crosseds or-s,and then averaged over the 30000 runs.

Thanks

Jamie

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# I Average number of times a random walk passes a point

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