  In a general simulation of random walking (with the angle of motion picked
uniformly), it can be seen that the probability of crossing a WiFi TX-RX link
is directly proportional to the per-step distance and inversely proportional to
the lateral dimension of the room. The asymptotic value of the said crossing
probability is derived using Perron-Frobenius theory to determine the limit
distribution of the said Markov model. Surprisingly, we can establish a
bijection to a scenario explored nearly 300 years ago by Georges-Louis Leclerc,
Comte de Buffon to get the result. Furthermore we can use the generalizations
of the latter problem to ascertain some interesting observations about the
original one.
