Theoretical Statistics and Mathematics Unit, ISI Delhi

October 9, 2013 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Rahul Roy,
Indian Statistical Institute, Delhi

Title:
Ranks of random matrices

Abstract of Talk

We discuss the result by Koml\'{o}s (1967, 1968, 1981) that a $n \times n$ matrix with i.i.d.
Bernoulli (1/2) entries is singular with a probability $O(n^{-1/2})$. In addition we talk about the Costello, Tao and Vu (2006) result that the random symmetric matrix with upper-diagonal
entries i.i.d. Bernoulli (1/2) also has full rank with probability 1.
We conclude with a recent result which studies the case of a $n \times n$ random matrix whose entries are i.i.d. Bernoulli ($n^{-\beta}$), $ \beta \in (0,1)$.
The last two results have a connection with Erd\"{o}s-Reny\'{i} random graphs.