What Are the Effects of Diffusing Boundaries on Random Walkers in 1D Lattices?

[NoobixCube]

Hi all,

I was wondering whether there was any work done on a random walker on a 1D lattice with diffusing boundaries?

Any links or suggestions would be great!

 

[mikeph]

I don't know what is a "diffusing boundary"?

But there is a lot of work done on the 1D discrete random walk as a Markov chain,

http://en.wikipedia.org/wiki/Random_walk

 

[SW VandeCarr]

In terms of net work done, the answer would be based on the amount of displacement from the origin over an interval of time. If the range is bounded, then the amount of net work done would approach zero as time approaches infinity.

EDIT: While I stand by what I said; there will be a finite non-zero amount of net work done with an absorbing boundary for a unit particle, equal to the displacement of the particle from the origin to the boundary. For a reflecting boundary the average net amount work done over time is zero.