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

On Dropping Needles and WiFi Link Crossing