An Introduction to Probability Theory and Its Applications, Volume II

TL;DR: An approach is described that is based on directly simulating the random walk associated with the waiting-time process of the GI/GI/1 queue, using a change of measure called delayed subex-potential twisting: an importance sampling idea recently developed and found useful in the context of M/ GI/1 heavy tailed simulations.

TL;DR: In this article, the following theorem is proved: for a finite set of cardinality n ≥ 2, and a family of subsets of the set, the equality holds if and only if for two different elements x, y of X, F = { F ⊆ X | x ∈ F, y ∈ X }.

TL;DR: This paper defines the class of greedy algorithms that use randomization and obtains the first randomized algorithm for the problem that uses at most 7l/5 + o(l) colors for coloring any set of paths of maximum load l on binary trees of depth O(l1/3-e), with high probability.

TL;DR: In this paper, the authors studied the Moran process on digraphs and showed that it is optimal, up to logarithmic factors, for any strongly connected n-vertex digraph with extinction probability Ω ( n − 1 / 2 ).