We study random cutting down of a rooted tree and show that the number of cuts is equal (in distribution) to the number of records in the tree when edges (or vertices) are assigned...
Limit theorems (including a Berry-Esseen bound) are derived for the number of comparisons taken by the Boyer-Moore algorithm for finding the occurrences of a given pattern in a ra...
: We study a model of random graphs, where a random instance is obtained by adding random edges to a large graph of a given density. The research on this model has been started by ...
Following the entropy method this paper presents general concentration inequalities, which can be applied to combinatorial optimization and empirical processes. The inequalities g...
: Consider ordinary bond percolation on a finite or countably infinite graph. Let s, t, a, and b be vertices. An earlier paper (J. Van den Berg and J. Kahn, Ann Probab 29 (2001), 1...