Solving random walk problems using resistive analogues

The classical method of solving random walk problems involves using Markov chain theory. When the particular random walk of interest is written in matrix form using Markov chain theory, the problem must then be solved using a digital computer. To solve all but the most trivial random walk problems by hand would be extremely difficult and time consuming. Very large random walk problems may even prove difficult to solve on the smaller digital computers. This paper intends to demonstrate a method that may be used to solve large random walk problems in a quick and economical manner. This alternate method uses resistive analogues and has the added feature of extracting particular solutions without having to completely solve the problem as would be necessary using a digital computer. Many analogues of random walks may also be quickly amended to include other random walks with relative ease using this alternate method of solution. Because this method uses nothing more than a power supply, a DC voltmeter and a set of resistors, the analogue of a particular random walk problem may be left set-up without incurring any loss of time or money on a digital computer. Once the resistors are mounted in a permanent fashion, the random walk analogues may also be used as an effective demonstration of random walk probabilities in the classroom