From social networks such as Facebook, the World Wide Web and the Internet, to the
complex interactions between proteins in the cells of our bodies, we constantly face the …

Upper bounds on probabilities of large deviations for sums of bounded independent random
variables may be extended to handle functions which depend in a limited way on a number …

Random graphs have proven to be one of the most important and fruitful concepts in modern
Combinatorics and Theoretical Computer Science. Besides being a fascinating study …

Consider the minimum spanning tree (MST) of the complete graph with n vertices, when
edges are assigned independent random weights. Endow this tree with the graph distance …

An assignment problem is the optimization problem of finding, in an m by n matrix of
nonnegative real numbers, k entries, no two in the same row or column, such that their sum …

We establish that in the large degree limit, the value of certain optimization problems on
sparse random hypergraphs is determined by an appropriate Gaussian optimization …

In their seminal paper introducing the theory of random graphs, Erd\H {o} s and R\'{e} nyi
considered the evolution of the structure of a random subgraph of $ K_n $ as the density …

We address the problem of evaluating the expected optimal objective value of a 0-1
optimization problem under uncertainty in the objective coefficients. The probabilistic model …

We consider percolation on high‐dimensional product graphs, where the base graphs are
regular and of bounded order. In the subcritical regime, we show that typically the largest …

It is known that many different types of finite random subgraph models undergo
quantitatively similar phase transitions around their percolation thresholds, and the proofs of …