Category Probability
Expectation of minimum of n i.i.d. uniform random variables
Let be independent uniform random variables from , and consider the random variable . Computing the expectation is a routine computation: . However, there a slick way of computing this expectation. Let be another uniform random variable in . Consider the probability . On the one hand due to symmetry, it is equal to , on […]
An observation on edge densities of the union of isomorphic copies of a fixed graph
Consider a fixed graph with vertices and edges respectively. Assume that is balanced which means that the maximum edge density among all possible subgraphs of is achieved from $H$. Take two copies of , call them and create a new graph . In case the two copies are edge disjoint then the edge density of […]
Giant component with Depth First Search
I just finished reading a short paper of Michael Krivelevich and Benny Sudakov, two leading experts in probabilistic combinatorics, which appeared in Arxiv about a month ago [1]. It is a simple proof of the classical result that the random binomial graph exhibits a phase transition around . When then the largest component has size […]
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