Compositions and Patricia Tries: No Fluctuations in the Variance!

We prove that the variance of the number of different letters in random words of length n, with letters i and probabilities 2-i attached to them, is 1 + o(1). Likewise, the variance of the insertion cost of symmetric Patricia tries of n random data is given by 1 + o(1). These two examples disprove popular belief that such quantities must always contain fluctuating terms.

• Type: Conference
• Year: 2004
• Where: ALENEX
• Authors: Helmut Prodinger
• Keywords: ALENEX 2004, ALENEX 2007, Random Words, Symmetric Patricia Tries, Variance