Doubly stochastic graph shifts are shown to be bounded in expectation and to converge to the mean for i.i.d. signals as neighborhoods grow, though the 'isometry' label is an overstatement.
Discrete Signal Processing on Graphs: Sampling Theory,
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A Class of Doubly Stochastic Shift Operators for Random Graph Signals and their Boundedness
Doubly stochastic graph shifts are shown to be bounded in expectation and to converge to the mean for i.i.d. signals as neighborhoods grow, though the 'isometry' label is an overstatement.