We provide a simple algorithmic argument to “explain” the concentration of measure phenomenon observed in the sum of independent random variables. Roughly speaking, we observe that without concentration of measure it would be possible to predict the outcome of a coin toss with probability greater than 1/2. We use this idea to derive an alternative proof of a Chernoff-Hoeffding bound for large d...

Recent research has studied how to measure the size of a search engine, in terms of the number of pages indexed. In this paper, we consider a di erent measure for search engines, namely the quality of the pages in a search engine index. We provide a simple, e ective algorithm for approximating the quality of an index by performing a random walk on the Web, and we use this methodology to compare...

We study the entanglement properties of random pure stabilizer states in spin1 2 particles. We obtain a compact and exact expression for the probability distribution of the entanglement values across any bipartite cut. This allows for exact derivations of the average entanglement and the degree of concentration of measure around this average. We also give simple bounds on these quantities. We f...