Abstract
A closed analytical formula is given for expected absolute difference to the power $a$ between two identical general random processes, when $a$ is an even positive number. As an application to sensor network, we analyze the following scenario: Black colored sensors $X_1,X_2,\dots,X_n$ and white colored sensors $Y_1,Y_2,\dots,Y_n$ are initially randomly placed according to general random process. We minimize the energy consumption of the transportation cost to the power $b>0$ of the maximal random bicolored matching.
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