Re: infinite square lattice of resistors

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding:

> > Is the above sketch sufficient?

> It probably is for someone cleverer than I, but I've never seen this one.
> Is it written up in more verbose (or algebrose) fashion somewhere? I'll
> never get another chance to teach it, but I'd like to know it anyway.
>
> Thanks,
>
> Leigh

Sorry, I don't know where it is written up outside of my own messy notes.
I'm sure that it *must* be published somewhere, but I haven't bothered to
look for where it might be found.  I know that a book by Frank Spitzer
entitled _Principles_of_Random_Walk_ does give the lattice Green's
function for a square (and maybe simple cubic too, but I don't recall for
sure, and don't have a copy of it) lattice, and shows how to do the sneaky
recursion technique along with the evaluation of the double integral along
a diagonal-directed displacement.  Spitzer uses the lattice Green's
function in the context of solving problems for various probabilities
pertaining to random walkers wandering through a regular lattice.

If there is some demand for the solution of this regular lattice resistor
network problem I suppose I could write up an electronically accessible
document about it.  But I don't have a lot of time for that at the
moment, and it might have to wait for a little while before I could get to
it.

David Bowman
David_Bowman@georgetowncollege.edu