Nicholas Pippenger

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math.PR2005

The Linking Probability of Deep Spider-Web Networks

Nicholas Pippenger

We consider crossbar switching networks with base $b$ (that is, constructed from $b \times b$ crossbar switches), scale $k$ (that is, with $b^{k}$ inputs, $b^{k}$ outputs and $b^{k}$ link…

math.PR2004

The average amount of information lost in multiplication

Nicholas Pippenger

We show that if X and Y are integers independently and uniformly distributed in the set {1, ..., N}, then the information lost in forming their product (which is given by the equiv…