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

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The discussion focuses on the effects of diffusing boundaries on random walkers in one-dimensional (1D) lattices. It highlights that significant research exists regarding 1D discrete random walks modeled as Markov chains. The net work done by a random walker is contingent on the boundaries; with absorbing boundaries, the net work equals the displacement from the origin, while reflecting boundaries yield an average net work of zero over time. The implications of these boundary conditions are critical for understanding the behavior of random walkers in various applications.

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NoobixCube
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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!
 
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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.
 
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