Electrical Engineering Systems Seminar
Hitting Times of Randomly Moving Hanoi Towers: Means and Moment Generating Functions
Abstract: We review Alekseyev's method for obtaining the mean of the hitting time of an n-disk randomly moving Hanoi Tower (RMHT) for selected initial and final states. Then we provide an alternative method for finding the mean time it takes a RMHT to transfer all n of its disks from peg 1 to peg 3, the task (sans random moves) originally posed by French mathematician Edouard Lucas in 1883 for his classic HT toy. In our alternative method the theorem for the mean commute time from any node A to any node B and then back to A of a random walk on an arbitrary bidirectional graph is combined with recursive application of the delta-to-wye transformation introduced in 1899 by Arthur E. Kennelly for analysis of three-phase electrical power distribution networks. (Incidentally, Kennelly is widely credited with having discovered the ionosphere). Finally, we extend Alekseyev's approach to obtain a recursion from n-1 to n of the MGFs of RMHT hitting times.
Caveat: This fascinating and enjoyable talk is believed to be of no practical use whatsoever!
Biosketches: Toby Berger is a Professor of Electrical and Computer Engineering at the University of Virginia, Charlottesville,VA and the Irwin and Joan Jacobs Professor of Engineering, Emeritus, Cornell University, Ithaca, NY. He specializes in information theory and its applications to problems in neuroscience. Berger, a recipient of a Guggenheim Fellowship, the ASEE's Terman Medal, the IEEE's Kirchmayer Graduate Teaching Award and its Hamming Medal, the IEEE Information Theory Society's Shannon Award and its A. D. Wyner Award, became a member of the NAE in 2006. Alekseyev, an Assistant Professor of Computer Science and Engineering at South Carolina, being much younger than Berger, has yet to receive such distinctions but will because he's also considerably brighter than Berger!
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