In this talk, we will show how a simple probabilistic question about a discrete random process, the "random walk", is related to the Dirichlet Problem - a classical question in analysis whose origins lie in thermodynamics. By first illustrating this question on a 1-dimensional gambler and a 2-dimensional thief, we will have the motivation and machinery to pose the DP on finite connected graphs.
This talk will be accessible to everyone almost surely, since the prerequisites are familiarity with two of the three: elementary combinatorics, the rush of gambling for money, and the lure of petty theft.