MATH 307 Lecture Notes - Lecture 38: Playstation 3
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Def xn probabilityof being at nodei after n certain amountof time. Sinceani"s are also probabilities oexni e l and xni 1. Xn11 i xn i pi t xn z piz txn3 piz pi piapb. P xn we get llnti pxn thesimilar relationin therecursion. In general for a system with k nodes wehave p pll 1712 iiiiii. Pik i l where it depij el in thesumof eachcolumn is 1 i e ftpij 1 for all j. Given an initialchoiceofsightseeing location where will the tourist most likely ends up eventually. This is equivalentto findingthe steadystate or large n behaviour ofthe system. Thetourist ends up in eitherlocation2 or location3 with 50 50 chances. It turns out that pkxo regardless whatxowestartfrom. If pkxo x as k x ftp. pkxo x. Iii pip xo x p iif p xo x i px x. Xis an eigenvector corresponding to theeigenvalue a l x.
